We illustrate some novel contraction and regularizing properties of the Heat flow in metric-measure spaces that emphasize an interplay between Hellinger-Kakutani, Kantorovich-Wasserstein Hellinger-Kantorovich distances. Contraction Hellinger-Kakutani distances general Csiszár divergences hold arbitrary do not require assumptions on linearity flow. style='text-indent...

We study two topologies $ \tau_{KR} and \tau_K on the space of measures a completely regular generated by Kantorovich–Rubinshtein Kantorovich seminorms analogous to their classical norms in case metric space. The topology coincides with weak nonnegative bounded uniformly tight sets measures. A sufficient condition is given for compactness topology. show that logarithmically concave measures, so...