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arXiv · 1902.05154

$L^1$-spaces of vector measures with vector density

Celia Avalos-Ramos
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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 $\nu_F$ with density $F$ defined on a $\delta$-ring is obtained. We present the existing connection between the spaces $L^1_w(\nu_F)$, $L^1(\nu_F)$ and $L^1(|\nu_F|)$ and the spaces of Dunford, Pettis or Bochner integrable functions.

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Celia Avalos-Ramos. 2019-02-13. $L^1$-spaces of vector measures with vector density. https://arxiv.org/abs/1902.05154

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