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arXiv · 1910.12341

On lifting invariant probability measures

Tomasz Cieśla
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Abstract

In this note we study when an invariant probability measure lifts to an invariant measure. Consider a standard Borel space $X$, a Borel probability measure $μ$ on $X$, a Borel map $T \colon X \to X$ preserving $μ$, a compact metric 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 fibers of $p$ are compact then $μ$ lifts to an $S$-invariant measure on $Y$.

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Tomasz Cieśla. 2020-06-03. On lifting invariant probability measures. https://doi.org/10.4064/ba200225-9-3

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