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- W1993518216 abstract "Let X1, X2, … be any sequence of random variables, and define Mn = max(X1, …, Xn), n ⩾ 1. Let {bn} be a real sequence such that bn → ∞. If {bn} is non-decreasing, it is well-known that P[Mn > bn i.o.] = P[Xn > bn i.o.]. This paper shows that this equality need not hold when {bn} is not monotone, even if X1, X2, … are i.i.d. Moreover, it is established that P[Mn > bn i.o.] = P[Xn > bn* i.o.], where bn* = infm⩾nbm, n⩾ 1." @default.
- W1993518216 created "2016-06-24" @default.
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- W1993518216 date "1996-03-15" @default.
- W1993518216 modified "2023-09-27" @default.
- W1993518216 title "Refinement of a zero-one law for maxima" @default.
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- W1993518216 doi "https://doi.org/10.1016/0167-7152(95)00045-3" @default.
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