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mona123

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dominate convergence theorem

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.

Fred

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Inscription : 26-09-2005

Messages : 7 352

Re : dominate convergence theorem

How did you prove the dominated convergence theorem? By using Fatou's lemma?