The Lebesgue Integral as the Almost Sure Limit of Random Riemann Sums

John C. Kieffer, Caslav V. Stanojevic
1982 Proceedings of the American Mathematical Society  
A method is given for generating random intermediate points for a sequence of partitions. For the corresponding random Riemann sums it is shown that they converge almost surely to the Lebesgue integral.
doi:10.2307/2043853 fatcat:xf6mnhq75rgavgagli6q3unyly