Chapter 7 - The Hahn–Jordan Decomposition Theorem, The Lebesgue Decomposition Theorem, and the Radon–Nikodym Theorem

Abstract

This chapter revolves around three classical theorems. In Section 7.1, it is shown that any σ-additive set function φ may be decomposed into the difference of two measures (i.e., φ is a signed measure). This is a brief description of the Hahn–Jordan Decomposition Theorem.