Some implications of Lebesgue decomposition

TL;DR

This paper generalizes Lebesgue decomposition to characterize weak compactness in the space of finitely additive measures, providing dual space representations and insights into measure structure.

Contribution

It introduces a generalized Lebesgue decomposition framework that offers new characterizations and structural results for finitely additive measures.

Findings

Characterization of weak compactness in the space ba

Representation of the dual space of ba

Structural insights into finitely additive measures

Abstract

Based on a generalization of Lebesgue decomposition we obtain a characterization of weak compactness in the space $ba$, a representation of its dual space and some results on the structure of finitely additive measures.