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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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The Lebesgue integral as the almost sure limit of random Riemann sums
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by John C. Kieffer and Časlav V. Stanojević PDF
Proc. Amer. Math. Soc. 85 (1982), 389-392 Request permission

Abstract:

A method is given for generating random intermediate points for a sequence of partitions. For the corresponding random Riemann sums it is shown that they converge almost surely to the Lebesgue integral.
References
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Additional Information
  • © Copyright 1982 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 85 (1982), 389-392
  • MSC: Primary 26A42; Secondary 60G46
  • DOI: https://doi.org/10.1090/S0002-9939-1982-0656109-X
  • MathSciNet review: 656109