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Given a compactly supported probability measure on a Riemannian manifold, we study the asymptotic speed at which it can be approximated (in Wasserstein distance of any exponent p) by finitely supported measure. This question has been studied under the names of ``quantization of distributions and, when p=1, ``location problem. When p=2, it is linked with Centroidal Voronoi Tessellations.
The theory of finitely supported algebraic structures represents a reformulation of Zermelo-Fraenkel set theory in which every construction is finitely supported according to the action of a group of permutations of some basic elements named atoms. I
In this paper it is proved that if a minimal system has the property that its sequence entropy is uniformly bounded for all sequences, then it has only finitely many ergodic measures and is an almost finite to one extension of its maximal equicontinu
Let $X$ be a compact metric space and let $Lambda$ be a $Z^k$ ($kge 1$) action on $X.$ We give a solution to a version of Voiculescus problem of AF-embedding: The crossed product $C(X)rtimes_{Lambda}Z^k$ can be embedded into a unital simple AF-algebr
We show that every finitely generated conical refinement monoid can be represented as the monoid $mathcal V(R)$ of isomorphism classes of finitely generated projective modules over a von Neumann regular ring $R$. To this end, we use the representatio
The study of universal approximation of arbitrary functions $f: mathcal{X} to mathcal{Y}$ by neural networks has a rich and thorough history dating back to Kolmogorov (1957). In the case of learning finite dimensional maps, many authors have shown va