A random approach to the Lebesgue integral |
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| Authors: | Jack Grahl |
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| Affiliation: | Mathematics Department, University College London, Gower Street, London WC1 6BT, United Kingdom |
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| Abstract: | We construct an integral of a measurable real function using randomly chosen Riemann sums and show that it converges in probability to the Lebesgue integral where this exists. We then prove some conditions for the almost sure convergence of this integral. |
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| Keywords: | Riemann integration Lebesgue integration Real function Random variable |
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