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A characterization of the barycentre

Part of: General convexity

Published online by Cambridge University Press:  26 February 2010

Bruno Girotto  and
Silvano Holzer
Bruno Girotto
Affiliation:
Dipartimento di Matematica Applicata “B. de Finetti”, University of Trieste, Piazzale Europa 1, 1-34127 Trieste, Italy.
Silvano Holzer
Affiliation:
Dipartimento di Matematica Applicata “B. de Finetti”, University of Trieste, Piazzale Europa 1, 1-34127 Trieste, Italy.
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Abstract

Given a Hausdorff topological vector space with dimensiongreater than one, the barycentre of simple masses can be seen as the unique associative, internal and continuous mapping defined on these masses. Moreover, if the associated dual space separates points, by extending the continuity property, one can characterize also the barycentre of masses with compact convex support.

MSC classification

Secondary: 52A07: Convex sets in topological vector spaces
Type
Research Article
Information
Mathematika , Volume 51 , Issue 1-2 , December 2004 , pp. 149 - 153
Copyright
Copyright © University College London 2004

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References

1.Girotto, B. and Holzer, S.. On the axiomatic treatment of the Ф-mean. J Ital. Statist. Soc., 3 (1995), 299–336.CrossRefGoogle Scholar
2.Girotto, B. and Holzer, S.. Weak convergence of masses: topological properties. Atti Sem. Mat. Fis. Univ. Modena, XLVIII (2000), 387–404.Google Scholar