DOI: 10.68381/jca25084 ISSN: 0944-6532
Fréchet Barycenters in the Monge-Kantorovich Spaces
Alexey Kroshnin
We consider the space
\mathcal{P}(X)
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
\mathcal{P}(X)
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
\mathcal{P}(X)
P
(
X
)
related to the transportation cost J.