Show that if for every then converges to zero a.e. This should follow from If is a sequence in is such that then for almost every . However, I don't see how to show this. I would appreciate some hints on how to proceed.
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Originally Posted by eskimo343 Show that if for every then converges to zero a.e. This should follow from If is a sequence in is such that then for almost every . However, I don't see how to show this. I would appreciate some hints on how to proceed. Not true, take if and otherwise. Then but
Originally Posted by putnam120 Not true, take if and otherwise. Then but That does not contradict the assertion that for almost every . Originally Posted by eskimo343 Show that if for every then converges to zero a.e. Let . Then (sum of geometric series). Define . Then , where denotes the measure. If then for all n>N. Therefore if then as . But is a null set.
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