
Journal of Convex Analysis 25 (2018), No. 4, [final page numbers not yet available] Copyright Heldermann Verlag 2018 Fréchet Barycenters in the MongeKantorovich Spaces Alexey Kroshnin Moscow Institute of Physics and Technology, Institute for Information Transmission Problems, 9 Institutskiy per., DolgoprudnyMoscow Region 141701, Russia kroshnin@phystech.edu We consider the space P(X) of probability measures on arbitrary Radon space X endowed with a transportation cost J(μ, ν) generated by a nonnegative continuous cost function. For a probability distribution on P(X) we formulate a notion of average with respect to this transportation cost, called here the Fréchet barycenter, prove a version of the law of large numbers for Fréchet barycenters, and discuss the structure of P(X) related to the transportation cost J. [ Fulltextpdf (179 KB)] for subscribers only. 