Suppose I have a sequence of random variables $X_i$ and a pair of scalars $a,b$ with the property that $$\lim_{i\to\infty} \Pr(a\leq X_i \leq b)\to1$$. What is the name for this kind of limiting statement? Could I say that "with probability one, we have $a\leq X_i \leq b$ as $i\to\infty$?"
2026-03-29 22:34:03.1774823643
Is this limit almost sure, in distribution, or other?
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