Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete

, Volume 55, Issue 1, pp 119–122

An elementary proof of the strong law of large numbers

  • N. Etemadi
Article

DOI: 10.1007/BF01013465

Cite this article as:
Etemadi, N. Z. Wahrscheinlichkeitstheorie verw Gebiete (1981) 55: 119. doi:10.1007/BF01013465
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Summary

In the following note we present a proof for the strong law of large numbers which is not only elementary, in the sense that it does not use Kolmogorov's inequality, but it is also more applicable because we only require the random variables to be pairwise independent. An extension to separable Banach space-valuedr-dimensional arrays of random vectors is also discussed. For the weak law of large numbers concerning pairwise independent random variables, which follows from our result, see Theorem 5.2.2 in Chung [1].

Copyright information

© Springer-Verlag 1981

Authors and Affiliations

  • N. Etemadi
    • 1
  1. 1.Mathematics DepartmentUniversity of Illinois at Chicago CircleChicagoUSA