On invariant probability measures I

Conditionally Invariant Probability Measures

V eronique Maume-Deschamps Section de Math ematiques, Universit e de Gen eve 2-4 rue du Lievre CP 240 Suisse. Abstract Let T be a measurable map on a Polish space X, let Y be a non trivial subset of X. We give conditions ensuring existence of conditionally invariant probability measures (to non absorption in Y). We also supply suucient conditions for these probability measures to be absolutely ...

Idempotent Probability Measures, I

The set of all idempotent probability measures (Maslov measures) on a compact Hausdorff space endowed with the weak* topology determines is functorial on the category Comp of compact Hausdorff spaces. We prove that the obtained functor is normal in the sense of E. Shchepin. Also, this functor is the functorial part of a monad on Comp. We prove that the idempotent probability measure monad conta...

Lasota-yorke Maps with Holes: Conditionally Invariant Probability Measures and Invariant Probability Measures on the Survivor Set

Let T : I ?! I be a Lasota-Yorke map on the interval I, let Y be a non trivial sub-interval of I and g 0 : I ?! R + , be a strictly positive potential which belongs to BV and admits a conformal measure m. We give constructive conditions on Y ensuring the existence of absolutely continuous (w.r.t. m) conditionally invariant probability measures to non absorption in Y. These conditions imply also...

INVARIANT MEASURES FOR MARKOV PROCESSES(i)

On Invariant Measures

Given a measurable transformation on a measure space one can ask whether or not there is an equivalent measure that is invariant under the transformation. This problem is discussed very thoroughly in Halmos' Lectures on ergodic theory, pp. 81-90, 97. The first result along these lines is due to E. Hopf who obtained necessary and sufficient conditions for the existence of a finite invariant meas...