## Bulletin of the Belgian Mathematical Society - Simon Stevin

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

#### 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.

#### Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 19, Number 2 (2012), 239-256.

Dates
First available in Project Euclid: 24 May 2012

https://projecteuclid.org/euclid.bbms/1337864270

Digital Object Identifier
doi:10.36045/bbms/1337864270

Mathematical Reviews number (MathSciNet)
MR2977229

Zentralblatt MATH identifier
1254.46045

#### Citation

Delgado, O.; Juan, M. A. Representation of Banach lattices as $L_w^1$ spaces of a vector measure defined on a $\delta$-ring. Bull. Belg. Math. Soc. Simon Stevin 19 (2012), no. 2, 239--256. doi:10.36045/bbms/1337864270. https://projecteuclid.org/euclid.bbms/1337864270