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mona123

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convergence

hi can someone please help me to prove this problem :
Let {fn} be a sequence of non-negative measurable functions on R such that fn → fa.e and lim∫R fn=∫R f < ∞.
prove  that lim∫E fn=∫E f   for each measurable set E ⊂ R,
Hint: Try to imitate the proof of the Dominated Convergence Theorem.
thanks in advance.

freddy

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Lieu : Paris

Inscription : 27-03-2009

Messages : 7 457

Re : convergence

Hello !

Don't you know that there are a lot of books in English about Measure's Theory ?

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De la considération des obstacles vient l’échec, des moyens, la réussite.

mona123

Invité

Re : convergence

hi freddy
please is the answer 4)9) in this web site file:///C:/Documents%20and%20Settings/ben%20said%20lotfi/Mes%20documents/Downloads/real%20analysis%20imti7an%20numero.pdf
is the solution of my problem?
thanks.

freddy

Membre chevronné

Lieu : Paris

Inscription : 27-03-2009

Messages : 7 457

Re : convergence

Hi mona,

I do not manage to read this document !

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De la considération des obstacles vient l’échec, des moyens, la réussite.