[리포트자료(data)]해석학(르벡지배수렴정리(整理) ) 리포트
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레포트자료,해석학,르벡지배수렴정리,레포트,기타,레포트
[레포트자료]해석학(르벡지배수렴정리) 레포트 , [레포트자료]해석학(르벡지배수렴정리) 레포트기타레포트 , 레포트자료 해석학 르벡지배수렴정리 레포트
5.6 Lebesgue Dominated Convergence Theorem
Let be a sequence of integrable functions which converges almost everywhere to a real-valued measurable function . If there exists an integrable function such that for all , then is integrable and
(5.4) .
PROOF.
(Cor.5.4)
: measurable, :integrable,
: integrable and
By redefining the functions , on a set of measure we may assume that the convergence takes place on all of .
∴ is integrable.
(Thm.5.5)
Since ,
(4.8 )
(5.5) ∴
Since ,
(5.6) ∴
∴
Dependence on a parameter
Defined function :
function for
(Cor.5.4)
If is measurable, is integrable, and ,
then is integrable, and
5.7 Corollary
Suppose that for some in
(5.7)
for each , and that there exists an integrable function on such that . Then
PROOF.
Let be a sequence in which converges to .
Let for , is integrable.
By Lebesgue Dominated Convergence Theorem,
.
5.8 Corollary
If the funct…(drop)
[리포트자료(data)]해석학(르벡지배수렴정리(整理) ) 리포트
[리포트자료(data)]해석학(르벡지배수렴정리(整理) ) 리포트
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레포트/기타
설명
다.
