Further randomization of Riemann sums leading to the Lebesgue integral

DOI10.1007/S13226-011-0030-8zbMath1260.28004OpenAlexW2039277528MaRDI QIDQ715613

A. Varsei, Elham Dastranj

Publication date: 31 October 2012

Published in: Indian Journal of Pure \& Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s13226-011-0030-8

zbMATH Keywords

random partitionsLebesgue integralrandom Riemann sumsRiemann sums

Mathematics Subject Classification ID

Measurable and nonmeasurable functions, sequences of measurable functions, modes of convergence (28A20) Integration with respect to measures and other set functions (28A25) Integrals of Riemann, Stieltjes and Lebesgue type (26A42)

Cites Work

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• A random approach to the Lebesgue integral
• The Lebesgue Integral as the Almost Sure Limit of Random Riemann Sums
• Randomly sampled Riemann sums and complete convergence in the law of large numbers for a case without identical distribution

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