On the law of large numbers for the bootstrap mean

Dedicated to my brother, Miklós Csörgő, for his sixtieth birthday.
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Abstract

Direct and elementary proofs are given for weak and strong laws of large numbers for bootstrap sample means under minimal moment conditions. Concerning the required rate of divergence of the bootstrap sample size, the strong laws obtained improve on those of Athreya (1983).

Ams 1980 Subject Classifications: Primary 60F15; Secondary 62G05

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Professor at large from the Bolyai Institute, University of Szeged, Hungary. Work done while a Visiting Professor at the Department of Statistics, University of North Carolina at Chapel Hill.

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