A NEW APPROACH TO THE RANDOM RIEMANN SUM
Elham Dastranj
Shahrood University of Technology
P.O. Box. 203-2308889030, Shahrood, IRAN
Abstract. In the investigation of convergence of random Riemann sums to the Lebesgue integral, the underlying measure is the Lebesgue one. In this paper we generalize the Lebesgue measure to an atom less measure that is positive on any interval with positive length.
AMS Subject classification: 60Hxx, 60Bxx, 60Gxx
Keywords and phrases: μ-integrable, Riemann sums, random Riemann sums, random Stieltjes sums, Lebesgue integral


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DOI: 10.12732/ijam.v26i3.2

Volume: 26
Issue: 3
Year: 2013