Transference of measures via disintegration
Volume 281 / 2025
Studia Mathematica 281 (2025), 1-51
MSC: Primary 46G10; Secondary 46A55, 28A35, 28A50
DOI: 10.4064/sm240513-27-8
Published online: 12 February 2025
Abstract
Given a compact space $K$ and a Banach space $E$ we study the structure of positive measures on the product space $K\times B_{E^*}$ representing functionals on $C(K,E)$, the space of $E$-valued continuous functions on $K$. Using the technique of disintegration we provide an alternative approach to the procedure of transference of measures introduced by Batty (1990). This enables us to substantially strengthen some of his results, to discover a rich order structure on these measures, to identify maximal and minimal elements and to relate them to the classical Choquet order.
