A proof of the convexity of the range of a nonatomic vector measure using linear inequalities
type: Item
instance of: scholarly article
title: A proof of the convexity of the range of a nonatomic vector measure using linear inequalities
zbMATH Open document ID: 0801.28003
DOI: 10.1016/0024-3795(94)90360-3
author: Alan J. Hoffman
author: Uriel G. Rothblum
published in: Linear Algebra and its Applications
publication date: 1994-11-24T00:00:00Z
review text: The paper provides a proof to the convexity part of A. A. Liapunov's theorem, that asserts that the range of an atomless finite dimensional vector measure is convex and compact. The present proof follows, e.g., the approach of \textit{P. R. Halmos} [Bull. Am. Math. Soc. 54, 416-421 (1948; Zbl 0033.052)] reducing however a key step that Halmos proves directly to a result on existence of extreme solutions of linear inequalities.
Mathematics Subject Classification ID: 28B05
zbMATH DE Number: 566109
zbMATH Keywords: Liapunov's convexity theorem
zbMATH Keywords: vector measure
MaRDI profile type: Publication
full work available at URL: 0024-3795(94)90360-3
OpenAlex ID: W2013690433
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description: scientific article; zbMATH DE number 566109