Geodesic
On lifting invariant probability measures
Tomasz Cieśla1
1 Department of Mathematics and Statistics McGill University 805, Sherbrooke Street West Montreal, Quebec, Canada H3A 2K6
Bulletin of the Polish Academy of Sciences. Mathematics, Tome 68 (2020) no. 1, pp. 69-74

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

We study when an invariant probability measure lifts to an invariant measure. Consider a standard Borel space $X$, a Borel probability measure $\mu $ on $X$, a Borel map $T \colon X \to X$ preserving $\mu $, a Polish space $Y$, a continuous map $S\colon Y \to Y$, and a Borel surjection $p \colon Y \to X$ with $p\circ S = T \circ p$. We prove that if the fibers of $p$ are compact then $\mu $ lifts to an $S$-invariant measure on $Y$.
DOI : 10.4064/ba200225-9-3
Keywords: study invariant probability measure lifts invariant measure consider standard borel space borel probability measure borel map colon preserving polish space continuous map colon borel surjection colon circ circ prove fibers compact lifts s invariant measure

Tomasz Cieśla 1

1 Department of Mathematics and Statistics McGill University 805, Sherbrooke Street West Montreal, Quebec, Canada H3A 2K6 
@article{10_4064_ba200225_9_3,
     author = {Tomasz Cie\'sla},
     title = {On lifting invariant probability measures},
     journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
     pages = {69--74},
     publisher = {mathdoc},
     volume = {68},
     number = {1},
     year = {2020},
     doi = {10.4064/ba200225-9-3},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/ba200225-9-3/}
}
TY  - JOUR
AU  - Tomasz Cieśla
TI  - On lifting invariant probability measures
JO  - Bulletin of the Polish Academy of Sciences. Mathematics
PY  - 2020
SP  - 69
EP  - 74
VL  - 68
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4064/ba200225-9-3/
DO  - 10.4064/ba200225-9-3
LA  - en
ID  - 10_4064_ba200225_9_3
ER  - 
%0 Journal Article
%A Tomasz Cieśla
%T On lifting invariant probability measures
%J Bulletin of the Polish Academy of Sciences. Mathematics
%D 2020
%P 69-74
%V 68
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4064/ba200225-9-3/
%R 10.4064/ba200225-9-3
%G en
%F 10_4064_ba200225_9_3
Tomasz Cieśla. On lifting invariant probability measures. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 68 (2020) no. 1, pp. 69-74. doi: 10.4064/ba200225-9-3

Cité par Sources :