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Lebesgue Measure and Integration on Subsets of R^d Kumar, Nand Kishor; Pokhrel, Chudamani; Yadav, Dipendra Prasad
Mikailalsys Journal of Mathematics and Statistics Vol 3 No 1 (2025): Mikailalsys Journal of Mathematics and Statistics
Publisher : Darul Yasin Al Sys

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.58578/mjms.v3i1.3958

Abstract

Henri Lebesgue, a French mathematician, discovered centuries ago that the Riemann Integral does not work well on unbounded functions. It prompts him to consider another way to integration known as Lebesgue Integral. This paper discusses the Riemann integral's shortcomings and introduce a more thorough concept of integration, the Lebesgue integral, repeated integration. There is also some debate about the Lebesgue measure, which determines the Lebesgue integral. Some examples are given, such as F_σ -set, G_δ -set and Cantor function. In this article, we first look into a unified theory for d-dimensional volume based on the concept of a measure, and then we will use that theory to build a stronger and more flexible theory for integration.

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