Abstract
In this paper we randomize in a particular way the sequence of partitions based on which the random Riemann sums are defined for a Lebesgue integrable function f on (0, 1). Convergence of such sums to the Lebesgue integral of f is investigated.
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Varsei, A., Dastranj, E. Further randomization of Riemann sums leading to the Lebesgue integral. Indian J Pure Appl Math 42, 493–509 (2011). https://doi.org/10.1007/s13226-011-0030-8
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DOI: https://doi.org/10.1007/s13226-011-0030-8