Measurable functions on charge spaces

Abstract

The concept of measurability of functions on a charge space is generalised for functions taking values in a uniform space. Several existing forms of measurability generalise naturally in this context, and new forms of measurability are proposed. Conditions under which the various forms of measurability are logically equivalent are identified. Applying these concepts to real-valued functions, some recent characterisations of measurable functions on a bounded charge space are generalised to the unbounded case.