Liapunov theorem for modular functions
type: Item
instance of: scholarly article
title: Liapunov theorem for modular functions
zbMATH Open document ID: 0841.28007
DOI: 10.1007/BF00676229
author: Anna Avallone
published in: International Journal of Theoretical Physics
publication date: 1996-07-18T00:00:00Z
review text: Generalizing the classical convexity theorem of Liapunov, the author proves as main theorem: If \(\mu: L\to \mathbb{R}^n\) is a nonatomic modular function on a complemented lattice satisfying the interpolation property (a condition weaker than \(\sigma\)-completeness), then \(\mu([0, a])\) is convex for any \(a\in L\). Hereby, complemented lattices of particular interest are orthomodular lattices.
reviewed by: Hans Weber
Mathematics Subject Classification ID: 28A60
Mathematics Subject Classification ID: 06C15
zbMATH DE Number: 844044
zbMATH Keywords: range
zbMATH Keywords: Lyapunov convexity theorem
zbMATH Keywords: convexity
zbMATH Keywords: modular function
zbMATH Keywords: complemented lattice
zbMATH Keywords: orthomodular lattices
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf00676229
OpenAlex ID: W2048650102
description: scientific article; zbMATH DE number 844044