Completeness of certain metric spaces of measures

Dorsch F (2022)

Publication Type: Journal article

Publication year: 2022


DOI: 10.1007/s00229-022-01399-7


We prove that the set of finite Borel measures on a separable and directionally limited metric space (X, d) is complete with respect to the metric d(A)(mu, v) = sup (A is an element of A)vertical bar mu (A) - nu(A)vertical bar for all families of Borel sets A that contain every closed ball of X. This allows to prove the existence and uniqueness of the invariant Borel probability measure of certain Markov processes on X. A natural application is a Markov process induced by a random similitude.

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Dorsch, F. (2022). Completeness of certain metric spaces of measures. Manuscripta Mathematica.


Dorsch, Florian. "Completeness of certain metric spaces of measures." Manuscripta Mathematica (2022).

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