Pointwise properties of convergence in probability

If a sequence of random variables Xn converges to X in probability we know little about the pointwise behavior Xn([omega]). In this note we show that if Xn converges to X quickly enough (for example, like n-[alpha] for [alpha] > 0) then, for almost all [omega], Xn([omega]) converges to X([omega]) outside a set of density zero.

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Year of publication:	1985
Authors:	Burton, Robert M.
Published in:	Statistics & Probability Letters. - Elsevier, ISSN 0167-7152. - Vol. 3.1985, 6, p. 315-316
Publisher:	Elsevier
Subject:	convergence in probability

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Type of publication:	Article
Source:	RePEc - Research Papers in Economics

Persistent link: https://ebvufind01.dmz1.zbw.eu/10005074710