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Proceedings of the American Mathematical Society

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

 

 

The Lebesgue integral as the almost sure limit of random Riemann sums


Authors: John C. Kieffer and Časlav V. Stanojević
Journal: Proc. Amer. Math. Soc. 85 (1982), 389-392
MSC: Primary 26A42; Secondary 60G46
MathSciNet review: 656109
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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.


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DOI: https://doi.org/10.1090/S0002-9939-1982-0656109-X
Keywords: Random Riemann sums, martingales, Lebesgue integral
Article copyright: © Copyright 1982 American Mathematical Society