When L¹ of a vector measure is an AL-space

Guillermo P. Curbera

Vol. 162 (1994), No. 2, 287–303

DOI: 10.2140/pjm.1994.162.287

Abstract

We consider the space of real functions which are integrable with respect to a countably additive vector measure with values in a Banach space. In a previous paper we showed that this space can be any order continuous Banach lattice with weak order unit. We study a priori conditions on the vector measure in order to guarantee that the resulting L¹ is order isomorphic to an AL-space. We prove that for separable measures with no atoms there exists a c₀-valued measure that generates the same space of integrable functions.

Mathematical Subject Classification 2000

Primary: 46E40

Secondary: 46B42, 46G10

Milestones

Received: 18 February 1992

Published: 1 February 1994