Thread: Fatou's Lemma valid for convergence in measure

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.

"There exists a subsequence such that



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."


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