Fréchet Barycenters and a Law of Large Numbers for Measures on the Real Line

Alexey Kroshnin, Andrei Sobolevski

Endow the space $\mathcal{P}(\mathbb{R})$ of probability measures on $\mathbb{R}$ with a transportation cost $J(\mu ,\nu )$ generated by a translation-invariant convex cost function. Fo…