2017/02/19 by Kroshnin, Alexey
#FOS: Mathematics #Probability (math.PR)
paper · doi:10.48550/arxiv.1702.05740
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.