Maharam-Types and Lyapunov's Theorem for Vector Measures on Locally Convex Spaces without Control Measures
Functional Analysis
2016-03-29 v1
Abstract
We formulate the saturation property for vector measures in lcHs as a nonseparability condition on the derived Boolean -algebras by drawing on the topological structure of vector measure algebras. We exploit a Pettis-like notion of vector integration in lcHs, the Bourbaki--Kluv\'anek--Lewis integral, to derive an exact version of the Lyapunov convexity theorem in lcHs without the BDS property. We apply our Lyapunov convexity theorem to the bang-bang principle in Lyapunov control systems in lcHs to provide a further characterization of the saturation property.
Keywords
Cite
@article{arxiv.1509.06965,
title = {Maharam-Types and Lyapunov's Theorem for Vector Measures on Locally Convex Spaces without Control Measures},
author = {M. Ali Khan and Nobusumi Sagara},
journal= {arXiv preprint arXiv:1509.06965},
year = {2016}
}