A Proof for the Fundamental Theorem of Calculus Using Hausdorff Measures

Abstract

This note contains a proof of the Fundamental Theorem of Calculus for the Lebesque-Bochner integral using Hausdorff measures (see 2.4). For the real case $(X=\mathbb{R})$, this proof uses only the basics from the Lebesque integral theory (see 2.6).