Dears,

I need the proof shows that the Fatou's Lemma remains valid if convergence almost everywhere is replaced by convergence in measure.

Best Regards.

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- March 16th 2012, 06:59 AMraedFatou's Lemma valid for convergence in measureDears,

I need the proof shows that the Fatou's Lemma remains valid if convergence almost everywhere is replaced by convergence in measure.

Best Regards. - March 16th 2012, 07:01 AMraedRe: Fatou's Lemma valid for convergence in measure
"There exists a subsequence such that

Attachment 23382

Since this subsequence also converges in measure to f, there exists a further subsequence, which converges pointwise to f almost everywhere, hence the previous variation of Fatou's lemma is applicable to this subsubsequence."

Attachment 23382

But I am not understand how we get the subsequence such that