Further randomization of Riemann sums leading to the Lebesgue integral
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.
Key wordsRandom partitions Riemann sums random Riemann sums Lebesgue integral
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- 1.M. Abramowitz and I. A. Stegun (Eds)., Stirling Numbers of the Second Kind, 24.1.4 in Handbook of Mathematical Functions With Formulas, Graphs, and Mathematical Tables, 5th printing. New York: Dover, (1972), 824–825.Google Scholar
- 4.O. Kallenberg, Random Measures, Academic Press, (1983).Google Scholar