Comparison and Equivalency of Riemann-integrable with Lebesgue- integrable

Abstract

This article compares Riemann integrability to Lebesgue integrability. A function must also be Lebesgue-integrable if it is Riemann-integrable, but opposite is not always true. The Lebesgue integral is a more generic and flexible idea that may be applied to a larger range of functions. Lebesgue integration provides a more general framework that expands integration options, particularly for more complicated functions. The equivalence of the two integrals is a difficult concept to grasp, and it is regularly covered in advanced real analysis courses.