A metric inequality characterizing barycenters and other Pettis integrals

Bilyeu, Russell G.

doi:10.1090/S0002-9939-1978-0500140-0

A metric inequality characterizing barycenters and other Pettis integrals
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by Russell G. Bilyeu

Proc. Amer. Math. Soc. 68 (1978), 323-326

DOI: https://doi.org/10.1090/S0002-9939-1978-0500140-0

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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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Integration von Funktionen deren Wert die Elemente eines Vektorraumes sind

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