When almost surely convergence implies convergence in $L^{p}$

Asked Aug 27 '17 at 18:38

Active Aug 27 '17 at 18:38

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I'm studying the types of convergence in probality and its relations and I have the following question:

What are the assumptions that together with almost surely convergence implies convergence in $L^p$?

Thanks.

asked Aug 27 '17 at 18:38

Mads C

2

Look at Vitali's convergence theorem for $L^p$. – Yousuf Soliman Aug 27 '17 at 18:48
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Have a look at this question: https://math.stackexchange.com/q/51502/ – saz Aug 27 '17 at 19:03
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Does this answer your question? If $f_k \to f$ a.e. and the $L^p$ norms converge, then $f_k \to f$ in $L^p$ – Marine Galantin Nov 15 '21 at 15:13

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