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