Teoría de La Medida Sesión 02
December 13, 2022 | Author: Anonymous | Category: N/A
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\MJUÎC LM IC NMLKLC Qmskño 25 Nkgumi Ãogmi Gcraîc Ãivcrmz
\mjrmncs lm aicsms njoñtjocs @ uo ajoduotj y G uoc `cnkikc lm sueajoduotjs lm @ @ . Lkrmnjs qum4 Lm…okakño 3. Qmc Qmc @ C 5 G . 3. G ms amrrclc ecdj ajnpimnmotjs sk Ca 5 G pcrc auciqukmr C 5. G ms amrrclc ecdj lk`mrmoakcs prjpkcs sk sk E C 5 G pcrc auciqukmr pcrmdc pcrmdc C6 E 5 G tci qum C E . 1. G ms amrrclc ecdj uokjoms (rmsp. kotmrsmaakjoms) …oktcs sk do>3 C d 5 G (rmsp. G ) pcrc auciqukmr ajimaakño …oktc C C 3 6 C5 6 4 4 4 6 Co lm mimnmotjs lm G .
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o d >3
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C d 5
3 C d 5 G (rmsp. 3 d >3 C d 5 G ) pcrc auciqukmr suamskño armakmotm (rmsp. lmarmakmotm) (Co )o5O , lm mimnmotjs lm G .
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Lm…okakño 5. Qmc Qmc @ @ uo ajoduotj y N N uoc `cnkikc lm sueajoduotjs lm @ @ . Qm lkam qum N N ms uoc aicsm njoñtjoc sk ms amrrclc ecdj uokjoms m kotmrsmaakjoms njoñtjocs.
Lm…okakño 1. Lclj uo ajoduotj @ y uoc `cnkikc crektrcrkc lm aicsms njoñtjocs lm sueajo duotjss lm @ duotj @ , sm lm…om ic kotmrsmaakño lm mscs aicsms njoñtjocs ajnj ic `cnkikc lm ajoduotjs qum pmrtmomamo c tjlcs miics.
Qm pumlm vmr `ãakinmotm qum ic kotmrsmaakño lm aicsms njoñtjocs, lm sueajoduotjs lm uo ajoduotj @ , `jrnc uoc aicsm njoñtjoc.
Lm…okakño `C 5 N(C) 4 C a 5 N(C)g. A ms motjoams uoc aicsm njoñtjoc. auciqukmr o 5 O, Mo m`matj, sk C sk C 3 C5 ms uoc suamskño lm mimnmotjs lm A motjoams, pcrc auciqukmr o a a sm tkmom C tkmom C o 5 N(C) y Co 5 N(C), csî qum o Co 5 N(C) y ( o Co ) > o Cao 5 N(C), pjr ij tcotj, o Co 5 A .
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Lm ic nksnc ncomrc sm lmnumstrc qum A ms amrrclc ecdj kotmrsmaakjoms njoñtjocs. Jevkcnmotm A ajotkmom c C, lm ncomrc qum motjoams sm pumlm ajoaiukr qum A ajotkmom c N(C), ij auci prumec qum N (C) ms amrrclc ecdj ajnpimnmotjs.
Rcrc lmnjstrcr qum N (C) ms amrrclc ecdj kotmrsmaakjoms …oktcs, smc4
A 3 > `C 5 N(C) 4 C Y E 5 N(C) pcrc auciqukmr E auciqukmr E 5 Cg. A 3 ms motjoams uoc aicsm njoñtjoc. motjoams, pcrc auciq auciqukmr ukmr Mo m`matj, sk C3 C5 ms uoc suamskño lm mimnmotjs lm A 3 motjoams, o 5 O y E 5 C, sm tkmom Co 5 N(C) y Co Y E 5 N(C), csî qum o Co 5 N(C) y ( o Co ) Y E > o (Co Y E ) 5 N(C), pjr ij tcotj, o Co 5 A 3 .
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Lm ic nksnc ncomrc sm lmnumstrc qum A 3 ms amrrclc ecdj kotmrsmaakjoms njoñtjocs.
1
Jevkcnmotm A 3 ajotkmom c C, lm ncomrc qum motjoams sm pumlm ajoaiukr qum A 3 ajotkmom c N(C), ms lmakr, pcrc auciqukmr C auciqukmr C 5 N(C) y E 5 C, sm tkmom C tkmom C Y E 5 N(C).
Qmc chjrc4
A 5 > `C 5 N(C) 4 C Y E 5 N(C) pcrc auciqukmr E auciqukmr E 5 N(C)g. A 5 ms motjoams uoc aicsm njoñtjoc. motjoams, pcrc auciq auciqukmr ukmr Mo m`matj, sk C3 C5 ms uoc suamskño lm mimnmotjs lm A 5 motjoams, o 5 O y E 5 N(C), sm tkmom tkmom Co 5 N(C) y Co Y E 5 N(C), csî qum o Co 5 N(C) y ( o Co ) Y E > o (Co Y E ) 5 N(C), pjr ij tcotj, o Co 5 A 5 .
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Lm ic nksnc ncomrc sm lmnumstrc qum A 5 ms amrrclc ecdj kotmrsmaakjoms njoñtjocs.
ajotkmom c C, lm C6 ncomrc qum ajotkmom c N(cCN ) sm(Ctkmom Ajnj A 3qum A 5pcrc A 5 ajotkmom Y E 5 ajoaiukr ), ms qum lmakr, aucimsqukmrc aucimsqukmrc C6 E 5 N (C)motjoams , sm tkmom C tkmomsm C pumlm N(C).
Ajrjicrkj Ajrj icrkj 3 (\mjrmn (\mjrmncc lm aicsms njoñ njoñtjoc tjocss pcrc ãigmercs ãigmercs)). Qmc Qmc @ uo ajoduotj y C uo ãigmerc lm sueajoduotjs lm @ @ , motjoams (C) > N(C).
Mi tmjrmnc 3 pumlm smr kosu…akmotm pums mo jacskjoms ôokacnmotm sm pumlm lmnjstrcr konmlkctcnmotm qum ic prjpkmlcl qum sm qukmrm prjecr ajnj vãiklc pcrc auciqukmr mimnmotj lm uoc uoc -ãigmerc sm aunpim pcrc uoc `cnkikc lm ajoduotjs qum ic gmomrco y qum ms amrrclc sñij ecdj kotmrsmaakjoms …oktcs (pjr mdmnpij, ic `cnkikc `jrnclc pjr tjljs ijs kotmrvcijs lm oônmrjs rmcims).
Lm…okakño =. Qmc Qmc @ uo ajoduotj y R uoc `cnkikc lm sueajoduotjs lm @. Qm lkam qum R ms uo -skstmnc sk ms amrrclc ecdj kotmrsmaakjoms …oktcs.
Lm…okakño 0. Qmc Qmc @ uo ajoduotj y L uoc `cnkikc lm sueajoduotjs lm @. Qm lkam qum L ms uo l-skstmnc sk @ @ 5 L y ms amrrclc ecdj lk`mrmoakcs prjpkcs y uokjoms njoñtjocs.
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Lm…okakño 7. Lclj uo ajoduotj @ y uoc `cnkikc crektrcrkc lm lm l-skstmncs lm sueajoduotjs lm @, sm lm…om ic kotmrsmaakño lm msjs l msjs l-skstmncs -skstmncs ajnj ic `cnkikc lm ajoduotjs qum pmrtmomamo c tjlcs miics. Qm pumlm vmr `ãakinmotm qum ic kotmrsmaakño lm l-skstmncs, lm sueajoduotjs lm uo ajoduotj uo l-skstmnc. -skstmnc. @, `jrnc uo l
Lm…okakño Lm… okakño 8. Lclc uoc ajim jimaa aakño kño G lm sue sueaajoduo joduotjs tjs lm uo ajoduo joduotj tj @, sm lm…om mi lskstmnc gmomrclj pjr G ajnj ic kotmrsmaakño lm tjljs ijs ijs l-skstmncs qum ajotkmomo c tjljs ijs mimnmotjs lm G y sm im lmojtc pjr l(G ).
Jesërvmsm qum ic lm…okakño cotmrkjr ms ajoskstmotm pums lclc auciqukmr ajimaakño R lm lm sueajo duotjs duot js lm uo ajodu ajoduotj otj @ mxkstm pjr ij nmojs uo l uo l-skstmnc -skstmnc qum ajotkmom c tjljs ijs ajoduotjs lm R , c scemr, mi l mi l-skstmnc -skstmnc `jrnclc pjr tjljs ijs sueajoduotjs lm @ .
Jesërvmsm tcnekëo qum mi l-skstmnc gmomrclj pjr uoc `cnkikc R lm sueajoduotjs lm uo ajoduotj @ ms mi nãs pmqumój l-skstmnc lm sueajoduotjs lm @ qum ajotkmom c tjljs ijs mimnmotjs lm R .
\mjrmnc 5. Qmc Qmc @ uo ajoduotj y R uo -skstmnc -skstmnc lm sueajoduotjs lm @, motjoams mi l-skstmnc l-skstmnc gmomrclj pjr R ms uo -skstmnc.
Lmnjstrcakño Qmc4 auciqukmr E 5 R g. A 3 > `C 5 l(R ) 4 C Y E 5 l(R ) pcrc auciqukmr E A 3 ms motjoams uo uo l-skstmnc. Mo m`matj, sk sk C3 C5 ms uoc suamskño lm mimnmotjs lm A 3 motjoams, pcrc auciqukmr o 5 O y E 5 R , sm tkmom Co 5 l(R ) y Co Y E 5 l(R ), csî qum l (R ), pjr ij tcotj, o Co 5 A 3 . Qmco chjrc l (R ) y ( o Co ) Y E > o (Co Y E ) 5 l( o Co 5 l( C6 A 5 A 3 tcims qum qum C A , motjoams C motjoams C66 A6 C Y E6 A Y E 5 l(R ) y C Y E A Y E pcrc auciqukmr E 5 R , csî qum auciqukmr qum A C 5 l(R ) y (A C) Y E > A Y E C Y E 5 l(R ), pjr ij C 5 A 3 . @kocinmotm, ms jevkj qum @ tcotj, A tcotj, A qum @ 5 A 3 .
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Jevkcnmotm A 3 ajotkmom c R , lm ncomrc qum motjoams sm pumlm ajoaiukr qum A 3 ajotkmom c l(R ), ms lmakr, pcrc auciqukmr C auciqukmr C 5 l(R ) y E 5 R , sm tkmom C tkmom C Y E 5 l(R ). Qmc chjrc4 auciqukmr E 5 l(R )g. A 5 > `C 5 l(R ) 4 C Y E 5 l(R ) pcrc auciqukmr E
=
A 5 ms motjoams uo uo l-skstmnc. Mo m`matj, sk sk C3 C5 ms uoc suamskño lm mimnmotjs lm A 5 motjoams, pcrc auciqukmr auciqukmr o 5 O y E 5 l(R ), sm tkmom tkmom Co 5 l(R ) y Co Y E 5 l(R ), csî qum l (R ), pjr ij tcotj, o Co 5 A 5 . Qmco chjrc l (R ) y ( o Co ) Y E > o (Co Y E ) 5 l( o Co 5 l( C6 A 5 A 5 tcims qum qum C A , motjoams C motjoams C66 A6 C Y E6 A Y E 5 l(R ) y C Y E A Y E pcrc C) Y E > A Y E C Y E 5 l(R ), pjr ij auciqukmr E auciqukmr E 5 l(R ), csî qum A qum A C 5 l(R ) y (A > A Y
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qum 5 A 5 . tcotj, A tcotj, A C 5 A 5 . @kocinmotm, ms jevkj qum Ajnj A 3 ajotkmom c c l(R ), sm tkmom qum A 5 ajotkmom c R , lm ncomrc qum motjoams sm pumlm ajoaiukr qum A 5 ajotkmom c c l(R ), ms lmakr, pcrc aucimsqukmrc aucimsqukmrc C6 E 5 l( l (R ), sm tkmom tkmom C Y E 5 l(R ).
Ajrjicrkj 5 (\mjrmnc lm aicsms njoñtjocs pcrc pk skstmncs). Qmc Qmc @ uo ajoduotj y R uo @ , motjoams l(R ) > ( -skstmnc lm sueajoduotjs lm @ (R ).
@uoakjoms …oktcnmotm clktkvcs y -clktkvcs Pcnjs c trcecdcr ajo mi ajoduotj lm oônmrjs rmcims mxtmolkljs, mi auci ajoskstm lmi ajoduotj lm oônmrjs rmcims y ljs mimnmotjs mspmakcims, 3 y 3 , ajo ijs aucims jpmrcrmnjs ecdj ics skgukmotms ajovmoakjoms4 Qk a Qk a 5 U, motjoams4
3 9 a 9 3, a 3 > 3, a + 3 > 3, a (3) > 3 sk a ? 2 2,, a (3) > 3 sk sk a a 9 2 2,, (2)(3) > (2) (2) (3) > 2, a 3
>
a 3
> 2,
(3) (3) > 3 + 3 > 3,
3 3 m 3 oj mstão lm…okljs. 3
U lmojtcrã ci ajoduotj U V `36 3g.
0
Lm…okakño ; (@uoakño …oktcnmotm clktkvc sjerm uo ãigmerc). Qmc Qmc @ uo ajoduotj y C uo ãigmerc lm sueajoduotjs lm @. Qm lkam qum uoc `uoakño oj omgctkvc omgctkvc 4 C 7! U ms …oktcnmot …oktc nmotmm clktkvc sk lclc auciq auciqukmr ukmr `cnki `cnkikc kc …oktc …oktc,, C3 6 4 4 4 6 Co , lm mimnmotjs lm C tci qum o
o f>3
Q R pcrc k 0 > d d,, motjoams ( ( C ) > C Y C > 6 pcrc k
d
f
f>3
( (Cf ).
Jesërvmsm Jesërv msm qum qum,, sk C ms uo ãigmerc lm sueajoduotjs lm @, pcrc prjecr qum uoc `uoakño 4 C 7! U ms …oktcnmotm clktkvc, ecstc ajo lmnjstrcr qum sk C y E sjo ljs ajoduotjs cdmojs lmi ãigmerc, motjoams motjoams ((C V E ) > ( (C) + (E ). \mokmolj mstc prjpkmlcl, ic clktkvklcl …oktc sm prumec ajo uo rczjocnkmotj lm koluaakño.
Lm…okakño 32 (@uoakño -clktkvc sjerm uo ãigmerc). Qmc Qmc @ uo ajoduotj y C uo ãigmerc lm sueajoduotjs lm @. Qm lkam qum uoc `uoakño oj omgctkvc omgctkvc 4 C 7! U ms -clktkvc sk ms …oktcnmot …oktc nmotmm clktkvc y lclc auciq auciqukmr ukmr `cnkik `cnkikc c ko…o ko…oktc ktc oun ounmr mrceim, ceim, C3 6 C5 6 4 4 4, 4, lm mimnmotjs lm
Q R Q C tci qum C Y C > 6 pcrc C 5 C, motjoams C > pcrc k 0 > d y 3
3
3
f
d
k
f
f>3
f>3
( (Cf ).
f>3
Lm…okakño 33 ( @uoakño -clktkvc sjerm uoc > uoc -ãigmerc). Qmc Qmc @ uo ajoduotj y > ãigmerc lm sueajoduotjs lm @ @. Qm lkam qum uoc `uoakño oj omgctkvc 4 4 > 7! U ms ms -clktkvc -clktkvc sk ms …oktcnmotm clktkvc y lclc auciqukmr `cnkikc ko…oktc ounmrceim, ounmrceim, C3 6 C5 6 4 4 4, 4, lm mimnmotjs
Q R lm > tci qum C Y C > 6, motjoams C > 3
3
k
d
f
( (Cf ).
f>3
f>3
Rrjpjskakño 3. Qmc Qmc @ uo ajoduotj, C uo ãigmerc lm sueajoduotjs lm @ y 4 C ! U uoc `uoakño `uoak ño oj omgctkv omgctkvc c …oktc …oktcnmo nmotm tm clktkvc clktkvc,, motjo motjoaams4 3. 3. Qk C6 E 5 C y C E , motjoams ( (C) (E ). 5. 5. Qk C3 6 4 4 4 6 Co 5
Lmnjstrcakño
o f>3
Q ( C, motjoams
f
o f>3
R C )
( (Cf ).
Qmco C6 E 5 C tcims qum C Qmco C6 qum C E , motjoams E motjoams E > > C C V(E C), csî qum qum ((E ) > ( (C)+ )+ (E C). Rjr ij tcotj, tcotj, ((C) (E ), yc qum qum ms oj omgctkvc. lm…ocnjs C 2 > 6, motjoams4 Qmco chjrc C chjrc C 3 6 4 4 4 6 Co 5 C y lm…ocnjs C
Q Q Q C C ) > ( R Q R C C > o f>3
o f>3
o f>3
f
f
f 3 d >2
f
d
C
f3 d >2 o f>3
d
( (Cf ).
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Ajrjicrkj 1. Qmc Qmc @ uo ajoduotj, C uo ãigmerc lm sueajoduotjs lm @ y y 4 C ! U uoc `uoakño `uoak ño oj omgctkv omgctkvc c …oktc …oktcnmo nmotm tm clktkvc clktkvc,, motjo motjoaams4 Qk C6 E 5 C, C E y (C) 9 3, motjoams4 (E C) > ((E ) (C). Rcrc auciqukmr pcrmdc C6 E 5 C tci qum (C) 9 3 j (E ) 9 3, sm tkmom4 (C V E ) > (C) + + (E ) (C Y E ).
\mjrmnc 1. Qmc Qmc @ uo ajoduotj, > uoc -ãigmerc lm sueajoduotjs lm @ y y 4 > ! U uoc `uoakño `uoak ño oj omgctkv omgctkvc c -clktkvc. Motjoams4 3. 3. Rcrc Rcrc auciqukmr suamskño armakmotm armakmotm (Co )o5O , lm mimnmotjs lm >, sm tkmom4 3 ( o>3 Co ) > ino!3 (Co ).
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(CO ) 9 5. 5. Rcrc Rcrc auciqukmr suamskño lmarmakmotm (C ( Co )o5O , lm mimnmotjs lm > > , tcims qum ( 3 pcrc ciguoc O 5 O, sm tkmom4 no 3 (Co ). ( 3 o>3 Co ) > i
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Lmnjstrcakño 3. Qmc ( Qmc (C Co )o5O uoc suamskño armakmotm lm mimnmotjs lm > . Qk Qk ((Co ) > 3 pcrc ciguoc o ciguoc o 5 O, motjoams i motjoams ino 3 ( o>3 Co ) > ino 3 (Co ).
3
Q
(Co ) > 3 y (
3
Q
Co ) > 36 csî qum
o>3
Qupjogcnjs chjrc qum qum ((Co ) 9 3 pcrc auciqukmr o auciqukmr o 5 O. Lm…ocnjs E Lm…ocnjs E 3 > C 3 y, pcrc aclc ajoduotjs E3 6 E5 6 4 4 4 pmrtmomamo c >, sjo o 5 `56 16 4 4 4g, Eo > Co C o3 . Motjoams ijs ajoduotjs 3
3
o>3
o>3
o
o
Q Q E . Csî qum4 R C > cdmojs pjr pcrmdcs y R Q Q ( (E ) ( (E ) > in E ) > C ) > ( ( R ( (C C ) > ( (E ) + in R V V(C ) (C > ( (E ) + in o>3
3
o
o>3
o
3
> ( (E3 ) + ino
3
o
o f>5
o f >3
3
3
3
o>3
f
o
o
3
f 3
3
(Co ) (C3 ) > ino
3
o
3
f
o f>5
f
f 3
)^
(Co ).
5. Qmc Qmc (Co )o5O suamskño lmarmakmotm lm mimnmotjs lm > tcims qum qum (CO ) 9 3 pcrc ciguoc O 5 O. suamskño (E EO +o )o5O Rcrc aclc f aclc f 5 `O + + 36 O + + 56 4 4 4g, lm…ocnjs E lm…ocnjs Ef > C O Cf . Motjoams ic suamskño ( 3 3 > C O o>O +3 Co , csî qum4 ms armakmotm y o>O +3 Eo > C
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Q
(
\
3
Co ) >
o>3
\
3
Co > ( (CO )
o>O +3
Q
3
Eo
o>O +3
8
> ( (CO ) ino
3
(EO +o ) > ( (CO ) ino
3
> ino!3 (CO +o ) > ino
3
(CO CO +o )
(Co ).
Mi cxkjnc lm mimaakño y mi imnc lm Tjro Cxkjnc lm mimaakño Qmc H uo ajoduotj `jrnclj pjr ajoduotjs oj vcaîjs, cdmojs pjr pcrmdcs. Mxkstm motjoams uo ajoduotj M, mi auci mstã `jrnclj pjr mxcatcnmotm uo mimnmotj lm aclc ajoduotj C 5 H.
Ajoduotjs pcrakcinmotm jrlmocljs Lm…okakño 35. Qm lkam qum uo ajoduotj @ , pcrc mi auci mstã lm…oklc uoc rmicakño lm jrlmo , ms pcrakcinmotm jrlmoclj sk sm sctks`camo ics skgukmotms prjpkmlclms4 3. 3. x x pcrc auciqukmr mimnmotj mimnmotj x 5 @. 5. Qk x6 x6 y6z 5 @ sjo tcims qum x y y y y z , motjoams x x z . 1. Qk x6 y 5 @ sjo tcims qum x y y x 0 > y, y , motjoams y y x. Qk, clmnãs, sm aunpim ic skgukmotm ic skgukmotm prjpkmlcl, sm lkam qum qum (@6 ) ms uo ajoduotj tjtcinmotm jrlmoclj4 y, y , motjoams mxcatcnmotm uoc lm ics skgukmotms ljs rmicakjoms ms vãiklc4 c) c) x y e) e) y x
Lm…okakño 31. Qk Qk (@6 ) ms uo ajoduotj pcrakcinmotm jrlmoclj y y x6 y 5 @, lkrmnjs qum x y sk x y y x x 0 > y. y .
Lm…okakño 3 V26 Qmc V26 3^, 3^, C uo ãigmer ãigmercc lm sueajodu sueajoduotj otjss lm lm y 4 4 C 7! V26 V26 3^ uoc 3^ uoc `uoakño …oktcnmotm clktkvc tci qum qum () > 3. 3. Rcrc aclc ajoduotj E ajoduotj E , lm…ocnjs4 k (E (E ) > sup ` (C) 4 C E y C 5 Cg m (E (E ) > o` o ` ` (C) 4 C E y C 5 Cg Mvklmotmnmotm sm tkmom4 2 k (E (E ) m (E (E ) 3 pcrc auciqukmr ajoduotj E ajoduotj E .
Rrjpjskakño 5. Qmco Qmco C6 E ljs sueajoduotjs lm lm tcims qum C Y E > 6, motjoams4 k (C (C) + + k (E (E ) k (C (C V E ) m
(C (C
V
E)
m (C (C) + + m (E (E )
Lmnjstrcakño qum A 3 C y 3. Rcrc lmnjstrcr qum qum k (C (C) + + k (E (E ) k (C (C V E ), smco smco A 3 6 A 5 5 C tcims qum Motjoams A 3 V A 5 C V E , csî qum4 A 5 E . Motjoams A + (A 5 ) k (C (C V E ) (A 3 V A 5 ) > (A 3) + Rjr ij tcotj4 k (C (C V E ) sup ` (A 3 ) + + (A 5 ) 4 A 3 C6 A 5 E y A 3 6 A 5 5 Cg @kdcolj A @kdcolj A 3 , jetmomnjs4 k (C (C V E ) (A 3 ) + sup ` (A 5 ) 4 A 5 E y A 5 5 Cg
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qum A 3 C. pcrc auciqukmr A auciqukmr A 3 5 C tci qum A Csî qum4 k (C (C V E ) sup ` (A 3 ) 4 A 3 C y A 3 5 Cg + sup ` (A 5 ) 4 A 5 E y A 5 5 Cg > k (C (C) + + k (E (E ) qum A 3 C y 5. Rcrc lmnjstrcr qum qum m (C (C V E ) m (C (C) + + m (E (E ), smco smco A 36 A 5 5 C tcims qum Motjoams A 3 V A 5 C V E , csî qum4 A 5 E . Motjoams A + (A 5 ) m (C (C V E ) (A 3 V A 5) (A 3 ) + Rjr ij tcotj4 m (C (C V E ) o` ` (A 3 ) + + (A 5 ) 4 A 3 C6 A 5 E y A 3 6 A 5 5 Cg @kdcolj A @kdcolj A 3 , jetmomnjs4 m (C (C V E ) (A 3 ) + o` o ` ` (A 5 ) 4 A 5 E y A 5 5 Cg qum A 3 C. pcrc auciqukmr A auciqukmr A 3 5 C tci qum A Csî qum4 m (C (C V E ) o` ` (A 3 ) 4 A 3 C y A 3 5 Cg + o` ` (A 5 ) 4 A 5 E y A 5 5 Cg > m (C (C) + + m (E (E )
\cnekëo, pcrc auciqukmr pcr lm sueajoduotjs lm , , C y E, E , tcims qum qum C Y E > 6 , sm aunpim ic skgukmotm lmskgucilcl4 k (C (C V E ) k (C (C) + + m (E (E ) m (C (C V E ) Qko mnecrgj, oj tmogj uoc lmnjstrcakño sknpim lm mstm rmsuitclj. Mo mi ikerj \hmjry ikerj \hmjry j` ahcrgms, C stuly j` …oktmiy cllktkvm nmcsurms , lm F. R. Q. Ehcsfcrc Ucj y N. Ehcsfcrc Ucj, sm hcam ic lmnjstrcakño njstrcolj prknmrj qum k y m sm pumlmo jetmomr lm ic skgukmotm ncomrc4 3
k (C (C) > sup f
R
o d >3
(E )
n d >3
R (C ) d
d
Ljolm mi suprmnj ms tjnclj sjerm tjlcs ics `cnkikcs …oktcs C 3 6 C5 6 4 4 4 6 Co y E3 6 E5 6 4 4 4 6 En lm mimnmotjs lm C tcims qum, pcrc cigôo oônmrj octurci f octurci f,, sm aunpic ic lmskgucilcl4 fK C +
dn>3
R
K Ed
do>3
R
K Cd
33 3
m (C (C) > o o` ` f
R
o d >3
(E )
n d >3
R (C ) d
d
Ljolm mi îo…nj ms tjnclj sjerm tjlcs ics `cnkikcs …oktcs C3 6 C5 6 4 4 4 6 Co y E3 6 E5 6 4 4 4 6 En lm mimnmotjs lm C tcims qum, pcrc cigôo oônmrj octurci f octurci f,, sm aunpic ic lmskgucilcl4 fK C +
dn>3
R
K Ed
do>3
R
K Cd
Hm mstclj eusacolj uoc lmnjstrcakño lkrmatc lm ic nmoakjoclc lmskgucilcl, pmrj oj ic hm moajotrclj. \ci vmz cigukmo lm ijs pcrtkakpcotms ic moaumotrm.
Ajrjicrkj 6 y C y C V E 5 C,motjoams4 (C V E ) > k (C (C) + + m (E (E )
Rrjpjskakño 1. Qmco Qmco C y E ljs sueajoduotjs lm lm pcrc ijs aucims mxkstmo A6 L 5 C tcims qum C C A , E L y A Y Y L > 6. Motjoams4 k (C (C V E ) > k (C (C) + + k (E (E ) m (C (C V E ) > m (C (C) + + m (E (E )
Lmnjstrcakño Rjr ic prjpjskakño ::, ôokacnmotm hcy qum lmnjstrcr ics skgukmotms lmskgucilclms4 k (C (C V E ) k (C (C) + + k (E (E ) m (C (C V E ) m (C (C) + + m (E (E ) Rcrc lmnjstrcr ic prknmrc lmskgucilcl, lclc " ? 2, smc M 5 C tci qum M C V E y (M ) k (C (C V E ) .
V L, M Y A C y M Y L E 6 csî qum4 Qm tkmom motjoams M motjoams M C V E A V V L)^ > (M Y A ) + (M ) > VM Y (A V + (M Y L) k (C (C) + + k (E (E ) Rjr ij tcotj4 k (C (C V E ) (M ) k (C (C) + + k (E (E ) @kocinmotm, ajnj mstc rmicakño sm aunpim pcrc auciqukmr " auciqukmr " ? 2, 2, sm tkmom4 k (C (C V E ) k (C (C) + + k (E (E ) Rcrc lmnjstrcr ic smguolc lmskgucilcl, lclc " ? 2, smc M 5 C tci qum M C V E y (M ) m (C (C V E ) + + ..
35
Qm tkmom motjoams M motjoams M Y A C y M Y L E 6 csî qum4
V L)^ > (M Y A ) + m (C (C V E ) + + (M ) VM Y (A V + (M Y L) m (C (C) + + m (E (E ) @kocinmotm, ajnj mstc rmicakño sm aunpim pcrc auciqukmr " auciqukmr " ? 2, 2, sm tkmom4 m (C (C V E ) m (C (C) + + m (E (E )
Mdmrakakj 3. Qmc Qmc C tci qum C 5 > C y lmojtmnjs pjr @ ci ãigmerc gmomrclc pjr pjr C y ijs mimnmotjs lm C. Lmnumstrc qum4
@ > `(C3 Y C) V (C5 Y Ca ) 4 C 3 6 C5 5 Cg
Rrjpjskakño Rrjpj skakño C y lmojtmnjs pjr @ ci ãigmerc gmomrclc pjr pjr C y ijs mimnmotjs lm C. Lm…ocnjs 4 @ 7!U lm ic skgukmotm ncomrc4 (E ) > k (E (E Y C) + + m (E (E Y Ca ) Motjoams ms uoc `uoakño oj omgctkvc y …oktcnmotm clktkvc tci qum4 (E ) > (E ) pcrc auciqukmr ajoduotj ajoduotj E 5 C.
Lmnjstrcakño Qmc E Qmc E 5 C6 ajnj E ajnj E > ((E E Y C) V (E Y Ca ), utkikzcolj mi ajrjicrkj (( ((E E Y C) V (E Y Ca )) > k (E (E Y C) + + m (E (E Y Ca ) > (E ) Rcrc lmnjstrcr ic clktkvklcl …oktc, smco A smco A66 L 5 @ tcims qum A qum A Y L > 6. A A y L sjo lm ic `jrnc4 sjo A A 36 A 5 5 C. A > ((A A 3 Y C) V (A 5 Y Ca ) sjo sjo L L 3 6 L5 5 C. L > (L3 Y C) V (L5 Y Ca ) sjo Ajnj A y L Ajnj A y L sjo sjo cdmojs, Qk mo iugcr lm A lm A 3 y A y A 5 tjncnjs tjncnjs A A 3 L3 y A y A 5 L5 , rmspmatkvcnmo rmspmatkvcnmotm, tm, ic prknmrc kgucilcl skgum skmolj vãiklc6 csî qum pjlmnjs csunkr qum A qum A 3 Y L3 > 6 y A 5 Y L5 > 6. \momnjs motjoams4
V L) > k ((A V L) Y C) + V L) Y Ca ) (A V ((A V + m (( ((A A V > k ((A ((A 3 V L3 ) Y C) + + m ((A ((A 5 V L5 ) Y Ca )
31
+ m ((A ((A 5 Y Ca ) V (L5 Y Ca )) > k ((A ((A 3 Y C) V (L3 Y C)) + + m (L (L5 Y Ca ) + m (A (A 5 Y Ca ) + + k (L (L3 Y C) + > k (A (A 3 Y C) + > k (A (A Y Y C) + + m (A (A Y Y Ca ) + + k (L (L Y C) + + m (L (L Y Ca ) > (A ) + + (L) Rjr ij tcotj, tcotj, ms …oktcnmotm clktkvc.
\mjrmnc C, @ mi ãigmerc gmomrclc pjr C y ijs mimnmotjs lm C y a2 5 Vk (C (C) 6 m (C (C)^ 4Mxkstm motjoams uoc `uoakño 4 4 @ 7! V26 V26 3^ tci 3^ tci qum4 3. 3. ms …oktcnmotm clktkvc. 5. 5. (E ) > (E ) pcrc auciqukmr E 5 C. 1. 1. (C) > a2 .
Lmnjstrcakño Lm…ocnjs Lm…ocnjs 3 4 @ 7! V2 V266 3^ 3^ y y 5 4 @ 7! V2 V266 3^ 3^ lm lm ic skgukmotm ncomrc4 3 (E (E ) > k (E (E Y C) + + m (E (E Y Ca ) 5 (E (E ) > k (E (E Y Ca ) + + m (E (E Y C) Motjoams Motjoams 3 y 5 sjo `uoakjoms oj omgctkvcs y …oktcnmotm clktkvcs tcims qum4 3 (E (E ) > (E ) y 5 (E (E ) > (E ), pcrc auciqukmr ajoduotj E ajoduotj E 5 C. Qmc c uo oônmrj rmci crektrcrkj mo mi kotmrvcij V2 Qmc V266 3^ y lm…ocnjs c 4 @ 7! V26 V26 3^ lm ic skgukmotm ncomrc4 c (E (E ) > c3 (E (E ) + (3 c) 5 (E (E ) Ajnj 3 y 5 sjo `uoakjoms oj omgctkvcs y …oktcnmotm clktkvcs, Ajnj clktkvcs, c tcnekëo ms oj omgctkvc y …oktcnmotm clktkvc. Qk E Qk E 5 C, sm tkmom4 c (E (E ) > c3 (E (E ) + (3 c) 5 (E (E ) > c (E ) + (3 c) (E ) > (E ) @kocinmotm4 c (C (C) > c3 (C (C) + (3 c) 5 (C (C) > ck ( C ( C)) + (3 c) m (C (C) > m (C (C) c (m (C (C) k ( ( C))
3<
Qk Qk k ( C ( C)) > m (C (C), tjnmnjs uo vcijr crektrcrkj lm c y lm…ocnjs > > c , motjoams4 (C) > m (C (C) > a2 Qk Qk k ( C ( C)) 0 > m (C (C), tjnmnjs c tjnmnjs c > >
m (C)a2 m (C)k ( C )
y lm…ocnjs lm…ocnjs > > c , motjoams4
(C) > m (C (C) c (m (C (C) k ( C ( C)) )) > m (C (C) (m (C (C) k ( C ( C)) )) m(Cm ()C)k a( C ) > a2 2
\mjrmnc =. Qmc (C) 6 m (C (C)^ )^ y R () () mi ajoduotj pjtmoakc Qmc C tci qum C 5 > C, a2 5 Vk (C lm . Mxkstm motjoams uoc `uoakño 4 R () 7! V2 V266 3^ tci 3^ tci qum4 3. 3. ms …oktcnmotm clktkvc. 5. 5. (C) > (C) pcrc auciqukmr C 5 C. 1. 1. (C) > a2 .
Lmnjstrcakño Lm…ocnjs4
H > `(G 6 n) 4 G ms uo ãigmerc lm sueajoduotjs lm lm 66 C G 6 C 5 G y n 4 n 4 G 7! V26 V26 3^ ms 3^ ms uoc `uoakño …oktcnmotm clktkvc tci qum4 3. n 3. n (E ) > (E ) pcrc auciqukmr E auciqukmr E 5 C. 5. 5. n n (C) > a2 .g 2
2
Rcrc ( G 6 n) 6 (G 6 n ) 5 H lm…ocnjs4 Rcrc ( auciqukmr E 5 G . (G 6 n) (G 2 6 n2 ) sk G G y n 2 (E ) > n (E ) pcrc auciqukmr E (H6 ) ms uo ajoduotj pcrakcinmotm jrlmoclj. Qmc F > `(G 6 n ) 4 5 g uoc aclmoc mo H. Ms lmakr, F H y (F6 ) ms uo ajoduotj tjtcinmotm jrlmoclj. Lm…ocnjs4
G >
Q
5
G
n 4 G 7! V26 V26 3^ lm 3^ lm ic skgukmotm ncomrc4 n (E ) > n (E (E ) sk E sk E 5 G .
3=
G ms motjoams uo ãigmerc lm sueajoduotjs lm y n ms uoc `uoakño …oktcnmotm clktkvc tci qum4 3. n 3. n (C) > (C) pcrc auciqukmr C auciqukmr C 5 C. 5. n 5. n (C) > a2 . Clmnãs, sm tkmom4 (G 6 n ) (G 6 n) pcrc auciqukmr auciqukmr 5 . Rjr ij tcotj, ( tcotj, ( G 6 n) ms uoc ajtc supmrkjr lm F . Rjr mi imnc lm Tjro, H tkmom uo mimnmotj ncxknci ( ncxknci ( Gnccxx 6 nnccxx ). Qk G nccxx 0 > R () (),, motjoams mxkstm P tci qum P 5 > Gnccxx . Qmc @ mi ãigmerc gmomrclc pjr P y ijs mimnmotjs lm Gnccxx , y n nccxx 4 @ 7! V26 V26 3^ uoc 3^ uoc `uoakño …oktcnmotm clktkvc qum mxtkmolm n mxtkmolm n nccxx lm G nccxx c @ . Motjoams4 cx 6 nn c cx x ) (@ 6 nn c cx x) (Gncx Ij auci ms uoc ajotrclkaakño, yc qum ( Gnccxx 6 nnccxx ) ms uo mimnmotj ncxknci lm H .
Csî qum, G nccxx > R () () y > > n n nccxx sctks`cam ics ajolkakjoms lmi mouoakclj.
Mdmnpij Lm…ocnjs > (26 (26 3^ 3^ y D ajnj mi ajoduo ajoduotj tj `jrnc `jrnclj lj pjr mi vcaîj y tjljs ijs kotmrv kotmrvcijs cijs lm ic `jrnc ( `jrnc (c6 c6 e^ , ljolm c ljolm c 9 e. Qmc C ic `cnkikc `jrnclc pjr ijs ajoduotjs lm ic `jrnc ajoduotjs mo D , cdmojs pjr pcrmdcs.
o d >3 d
Q
K ljolm ljolm o o 5 O y K y K 3 6 4 4 4 6 Ko sjo
C ms uo ãigmerc lm sueajoduotjs lm . . Rcrc aclc kotmrvcij kotmrvcij K 5 D , lmojtmnjs pjr b (K ) c ic ijogktul lmi kotmrvcij kotmrvcij K K y lm…ocnjs b (6) > 22.. Rcrc aclc C aclc C > >
o d >3 d
Q
lm…ocnjs ((C) > K 5 C, lm…ocnjs
o d >3
R
b b((K d ).
Ic `uoakño `uoakño 4 4 C 7! U ms oj omgctkvc, …oktcnmotm clktkvc y y () > 3. 3.
30
Qmc Q mi ajoduotj lm ijs oônmrjs rcakjocims ajotmokljs mo mi kotmrvcij (2 kotmrvcij (266 3^. 3^. Motjoams4 3. Q 5C > . 5. 5. k (Q) > 2 y m (Q) > 3. Rjr ij tcotj, pcrc auciqukmr a2 5 V2 V266 3^ 3^,, mxkstm uoc `uoakño `uoakño 4 4 R () 7! V26 V26 3^ tci 3^ tci qum4 3. 3. ms …oktcnmotm clktkvc. 5. 5. (C) > (C) pcrc auciqukmr C auciqukmr C 5 C. 1. 1. (Q) > a2 .
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