Show that if is a sequence in is such that then for almost every . This looks simple to prove. However, I do not see how to prove this right now. Any hints on how to proceed would be appreciated.
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Originally Posted by pascal4542 Show that if is a sequence in is such that then for almost every . This looks simple to prove. However, I do not see how to prove this right now. Any hints on how to proceed would be appreciated. You probably know that if is nonnegative and , then for almost every (this is almost by definition of the integral). Then apply that to ... (You will need the monotone convergence theorem to justify the computation of )
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