A General Hewitt-Yosida Decomposition

Abstract

In 1952, E. Hewitt and K. Yosida [3] proved that a bounded, finitely additive real-valued set function has a unique representation as the sum of a countably additive function and a “purely finitely additive” function.Below, using a variation of the Carathéodory process we give a suitable generalization to s-bounded vector-valued set functions. In fact, since the methods do not rely on scalar multiplication, we give the result for commutative Hausdorff topological groups.