On the regular representation of measures

Jürgen Jost, Rostislav Matveev, Jacobus Willem Portegies, and Christian S. Rodrigues

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Submission date: 11. Oct. 2016
Pages: 21
published in: Communications in analysis and geometry, 27 (2019) 8, p. 1799-1823 
DOI number (of the published article): 10.4310/CAG.2019.v27.n8.a5
Bibtex
MSC-Numbers: 37C40, 49K45, 49N60
Keywords and phrases: Representation of measures, Markov chain, random maps
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Abstract:
We give sufficient conditions for a parametrised family of probability measures on a Riemannian manifold with boundary to be represented by random maps of class C^k. The conditions allow for the probability densities to approach zero towards the boundary of the manifold. We also formulate two obstructions to regular representability.