Prove that if is a sequence in with for all then converges to zero a.e.

This should follow from this:

If is a sequence in is such that then for almost every .

However, I do not see how this would follow. How do I prove this?

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- December 13th 2009, 01:48 PMcanberra1454Sequence, Lebesgue Space
Prove that if is a sequence in with for all then converges to zero a.e.

This should follow from this:

If is a sequence in is such that then for almost every .

However, I do not see how this would follow. How do I prove this? - December 13th 2009, 01:53 PMLaurent
Why not apply the quoted result to ?... Try to find how to conclude from there.