On Spaces of Bochner and Pettis Integrable Functions and Their Set-Valued Counterparts

Abstract

The aim of this paper is to give a brief summary of the Pettis and Bochner integrals, how they are related, how they are generalized to the set-valued setting and the canonical Banach spaces of bounded maps between Banach spaces that they generate. The main tool that we use to relate the Banach space-valued case to the set-valued case, is the Rådström embedding theorem.KeywordsAbsolutely summing operatorBanach latticeBanach spaceBochner integralPettis integral