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

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

2012-03-07

arxiv.org/abs/1203.1462v1

Mathematics

Classical Analysis and ODEs

Scientific paper

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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