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Sep 16, 2015 at 13:05 comment added Iosif Pinelis As I said, I am wondering what the relation is.
Sep 16, 2015 at 13:02 comment added Igor Rivin @IosifPinelis The theorem is on laws of large numbers in the absense of moment conditions. Are you saying this is not related to the question?
Sep 16, 2015 at 12:49 comment added Iosif Pinelis That theorem is about sequences $(X_j)_{j\in\mathbb N}$ of i.i.d. r.v.'s with $EX_1^+={EX_1}^-=\infty$, whereas the question here appears to be about triangular arrays $(X_{n,i}\colon n\in\mathbb{N},i=1,\dots,n)$ of r.v.'s with finite (albeit growing with $n$) first two moments. I am wondering how that theorem is related to the question.
Sep 15, 2015 at 15:02 history answered Igor Rivin CC BY-SA 3.0