Title of article :
A Note on the Convergence of Random Riemann and Riemann-Stieltjes Sums to the Integral
Author/Authors :
Dastranj ، E. - Shahrood University
Abstract :
Convergence in probability of random Riemann sums of a Lebesgue integrable function on [0; 1) to the integral has been proved. In this article we generalize the result to an abstract probability space under some natural conditions and we show L1- convergence rather than convergence in probability..
Keywords :
System of partitions , random Riemann Sums , Random Riemann , Stieltjes Sums , L1 Convergence , Integral
Journal title :
General Mathematics Notes
Journal title :
General Mathematics Notes