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Results tagged with limits-and-convergence
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user 490637
Convergence of series, sequences and functions and different modes of convergence.
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Convergence in probability of a supremum
Let $A>0$ be fixed and consider $X_1,\ldots$ i.i.d. nonnegative random variables such that $E[1/X_1]<\infty$.
Is is true that $$\sup_{a\in \big (0,\frac A{\sqrt n} \big]} \sum_{i=1}^n 1_{X_i>a} \frac{ …
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