Math of QM: Appendix on Absolutely Continuous Functions, part 1

Decomposition of general distribution functions and their integrals into atomic part and continuous part; motivation for the relevance of absolutely continuous part.

This is part 5 of the Appendix in the lecture series "Mathematical Aspects of Quantum Mechanics" of Roland Speicher in the winter term 2020/21 at Saarland University, Germany. The Appendix, which is split into 6 parts, provides some basic background information about Lebesgue-Stieltjes integration and absolutely continuous functions.