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.

Printable View

- Mar 16th 2012, 07:59 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. - Mar 16th 2012, 08:01 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