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 Feb11 awarded Notable Question Dec15 awarded Nice Question Nov14 awarded Notable Question Oct5 awarded Famous Question Sep24 awarded Autobiographer Sep16 awarded Popular Question Sep1 awarded Yearling Jul12 revised The variational formulation of entropy edited body Jul11 asked The variational formulation of entropy Jul8 awarded Nice Question Jul2 awarded Notable Question Jul2 awarded Curious Jul2 awarded Inquisitive Jun15 awarded Popular Question May16 revised If the sum of two independent random variables is in $L^2$, is it true that both of them are in $L^1$? deleted 148 characters in body May14 accepted If the sum of two independent random variables is in $L^2$, is it true that both of them are in $L^1$? May13 revised If the sum of two independent random variables is in $L^2$, is it true that both of them are in $L^1$? added 148 characters in body May13 comment If the sum of two independent random variables is in $L^2$, is it true that both of them are in $L^1$? @Batman That's why proving $X$ and $Y$ are in $L^1$ should be an easier task, isn't it? May13 comment If the sum of two independent random variables is in $L^2$, is it true that both of them are in $L^1$? Can you give an example s.t. $\mathbb E(X+Y)^2 < \infty$ but $\mathbb E X = \infty$ and $\mathbb E Y = \infty$? May12 comment 1D biased random walk - is the event of infinte many returns a tail event? You should check Hewitt–Savage zero–one law - en.wikipedia.org/wiki/…