A New Proof of the Monotone Convergence Theorem of Lebesgue Integral on \sigma-Class

TL;DR

This paper presents a novel proof of the monotone convergence theorem for Lebesgue integrals specifically on -class, offering an alternative approach to existing proofs.

Contribution

It introduces a new proof technique for the monotone convergence theorem applicable to -class, expanding the theoretical understanding of Lebesgue integration.

Findings

Provides a new proof of the monotone convergence theorem on -class

Enhances theoretical foundations of Lebesgue integration

Offers potential for simplified teaching and further research

Abstract

In this short note a new proof of the monotone con- vergence theorem of Lebesgue integral on \sigma-class is given.