Kuelbs–Steadman Spaces for Banach Space-Valued Measures

Abstract

We introduce Kuelbs–Steadman-type spaces ( K S p spaces) for real-valued functions, with respect to countably additive measures, taking values in Banach spaces. We investigate the main properties and embeddings of L q -type spaces into K S p spaces, considering both the norm associated with the norm convergence of the involved integrals and that related to the weak convergence of the integrals.