Year: 2019
Type: preprint
Abstract: Let $F$ be a function with values in a Banach space. When $F$ is locally (Pettis or Bochner) integrable with respect to a locally determined positive measure, a vector measure $ν_F$ with density $F$ defined on a $δ$-ring is obtained. We present the existing connection between the spaces $L^1_w(ν_F)$, $L^1(ν_F)$ and $L^1(|ν_F|)$ and the spaces of Dunford, Pettis or Bochner integrable functions.
Source: arXiv (Cornell University)
Author: Avalos-Ramos, Celia
Institution: Universidad de Guadalajara
Language: English
Topic: Advanced Banach Space Theory
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2913724733