### Representation of Banach lattices as $L_w^1$ spaces of a vector measure defined on a $\delta$-ring

O. Delgado and M. A. Juan
Source: Bull. Belg. Math. Soc. Simon Stevin Volume 19, Number 2 (2012), 239-256.

#### Abstract

In this paper we prove that every Banach lattice having the Fatou property and having its $\sigma$-order continuous part as an order dense subset, can be represented as the space $L_w^1(\nu)$ of weakly integrable functions with respect to some vector measure $\nu$ defined on a $\delta$-ring.

First Page:
Primary Subjects: 46G10
Secondary Subjects: 46E30, 46B42