Compositions of nuclear maps with vector measures and measurable functions

Abstract

The properties of the compositions of nuclear maps, between two locally convex spaces, with vector measures and measurable functions are investigated. The composition with a vector measure has improved variational properties and a precompact range. The measurability and integrability properties of the composition of a nuclear map with a measurable function are vastly improved. The properties of nuclear space-valued measures and measurable functions are also investigated.