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arXiv · 1203.1462

A simple proof of the Fundamental Theorem of Calculus for the Lebesgue integral

Rodrigo López Pouso
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Abstract

This paper contains a new elementary proof of the Fundamental Theorem of Calculus for the Lebesgue integral. The hardest part of our proof simply concerns the convergence in ${\rm L}^1$ of a certain sequence of step functions, and we prove it using only basic elements from Lebesgue integration theory.

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Rodrigo López Pouso. 2012-03-07. A simple proof of the Fundamental Theorem of Calculus for the Lebesgue integral. https://arxiv.org/abs/1203.1462

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