Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete

, Volume 55, Issue 1, pp 119-122

First online:

An elementary proof of the strong law of large numbers

  • N. EtemadiAffiliated withMathematics Department, University of Illinois at Chicago Circle

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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].