Special Session 12: 

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

Nobusumi Sagara
Hosei University
Japan
Co-Author(s):    
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.