A Generalization of Riemann Sums

TL;DR

This paper extends the classical convergence property of Riemann sums for continuous functions, providing a broader framework and demonstrating applications of this generalization.

Contribution

It introduces a generalized form of Riemann sums that applies beyond equidistant subdivisions, expanding the theoretical understanding of integral approximation.

Findings

Generalized Riemann sums converge to the integral under broader conditions

Applications demonstrate usefulness in various mathematical contexts

Extends classical convergence results to new settings

Abstract

We generalize the property that Riemann sums of a continuous function corresponding to equidistant subdivision of an interval converge to the integral of that function, and we give some applications of this generalization.