Here we give an estimation of the modular convergence of translated equidis- tant Riemann sums to the integral of a function belonging to a modular space. Thus we extend some previous results by Fominykh and Kaminska-Musielak.
"Approximation by Riemann sums in modular spaces." Hokkaido Math. J. 30 (2) 253 - 267, June 2001. https://doi.org/10.14492/hokmj/1350911952