Decomposability, Convexity and Continuous Linear Operators in $L^1(\mu ,E)$: The Case for Saturated Measure Spaces

Abstract

Motivated by the Lyapunov convexity theorem in infinite dimensions, we extend the convexity of the integral of a decomposable set to separable Banach spaces under the strengthened notion of nonatomicity of measure spaces, called "saturation", and provide a complete characterization of decomposability in terms of saturation.

arXiv admin note: text overlap with arXiv:1902.09533, arXiv:1610.04776