Year: 2026
Type: preprint
Abstract: We extend Rainwater's theorem that, for Baire measures on a compact Hausdorff space,a measure singular with respect to any measure from a $w^*$-compact convex set $M$ of probability measures sits on a Baire set which is $μ$-null for every $μ\in M$. Our main result shows that this statement holds under the weaker assumption of convex analyticity of $M$. In the standard way, this extends the Glicksberg--König--Seever decomposition theorem. We also give conditions for our results to hold for sets of signed measures.
Source: arXiv (Cornell University)
Author: Preiss, David
Language: English
Topic: Advanced Banach Space Theory
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7214979659