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

Rodrigo López Pouso

Published 2012-03-07Version 1

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.