Existence de probabilités topologiquement compatibles semi-canoniques sur les espaces métriques compacts

Details Existence de probabilités topologiquement compatibles semi-canoniques sur les espaces métriques compacts Existence de probabilités topologiquement compatibles semi-canoniques sur les espaces métriques compacts

2011-08-10

arxiv.org/abs/1108.2181v1

Mathematics

Probability

34 pages, 1 figure

Scientific paper

This article describes a method for constructing a relevant probability measure in any nonempty compact metric space. This measure possesses invariance properties with respect to maps defined in a natural way in such spaces. Its definition uses a generalized notion of limit in zero in the ring of borned maps. In a second time, we give some properties of this measure. Then we exhibit some nontrivial examples of compact metric spaces and we use our theorem to obtain unusual probability spaces. We also describe some maps letting these probability measures invariant.

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