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
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
MSC-Numbers: 37C40, 49K45, 49N60
Keywords and phrases: Representation of measures, Markov chain, random maps
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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 Ck. The conditions allow for the probability densities to approach zero towards the boundary of the manifold. We also formulate two obstructions to regular representability.