A random approach to the Lebesgue integral

DOI10.1016/J.JMAA.2007.07.057zbMath1147.28001OpenAlexW2027324026MaRDI QIDQ2467772

Jack Grahl

Publication date: 28 January 2008

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2007.07.057

zbMATH Keywords

Almost sure convergenceRandom Riemann integral

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)

Related Items (2)

Functions not first-return integrable ⋮ Further randomization of Riemann sums leading to the Lebesgue integral

Cites Work

• Unnamed Item
• A first return examination of the Lebesgue integral.
• Almost every sequence integrates
• First-return limiting notions in real analysis
• The Lebesgue Integral as the Almost Sure Limit of Random Riemann Sums
• Probability: A Graduate Course
• Randomly sampled Riemann sums and complete convergence in the law of large numbers for a case without identical distribution

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