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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A metric inequality characterizing barycenters and other Pettis integrals


Author: Russell G. Bilyeu
Journal: Proc. Amer. Math. Soc. 68 (1978), 323-326
MSC: Primary 46G10
MathSciNet review: 0500140
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Abstract: Certain Pettis integrals, including barycenters of probability measures on weakly compact subsets of Banach spaces, are characterized by an integral inequality which refers only to distances between points, avoiding any reference to the linear structure of the Banach space. This is an elaboration of the Mazur-Ulam discovery that the metric determines the linear structure.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1978-0500140-0
PII: S 0002-9939(1978)0500140-0
Keywords: Banach, barycenter, Pettis integral
Article copyright: © Copyright 1978 American Mathematical Society