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Questions tagged [almost-everywhere]

For questions about the concept of "almost everywhere", that is, questions about properties which holds everywhere, except on a set of measure 0. This is involved in probability theory as well as in the case of infinite measure space. Use the appropriate tags to specify the context.

This is a concept in probability and measure theory. Something is said to hold almost everywhere if the set on which it does not hold has measure 0. This is involved in probability theory as well as in the case of infinite measure space. Use the appropriate tags to specify the context.

484 questions
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Almost surely tends to problem

$\dfrac{\max|X_i|}{n}$ tends almost surely to $0$ where '$X_i$' has a distribution with finite $2$nd order moments. Can anyone here provide me with the proof?
Dwaipayan Gupta
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proposition of borel-cantelli lemma

I know by the Borel-Cantelli lemma that for all $\epsilon > 0, \ \sum_{n=1}^{\infty} P(|X_n|>\epsilon)<\infty \Rightarrow X_n \xrightarrow{a.e.} 0$. But, how can I prove that the if and only if condition holds, which means that also holds that if…
NHB
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