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arXiv · 1903.04301

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

Nobusumi Sagara
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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.

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Nobusumi Sagara. 2019-03-08. Decomposability, Convexity and Continuous Linear Operators in $L^1(\mu,E)$: The Case for Saturated Measure Spaces. https://arxiv.org/abs/1903.04301

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