# Wydawnictwa / Czasopisma IMPAN / Bulletin Polish Acad. Sci. Math. / Wszystkie zeszyty

## On lifting invariant probability measures

### Tom 68 / 2020

Bulletin Polish Acad. Sci. Math. 68 (2020), 69-74 MSC: Primary 37L40. DOI: 10.4064/ba200225-9-3 Opublikowany online: 6 April 2020

#### Streszczenie

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 $Y$.

#### Autorzy

• Tomasz CieślaDepartment of Mathematics and Statistics
McGill University
805, Sherbrooke Street West