Geodesic
A nonsingular action of the full symmetric group admits an equivalent invariant measure
Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 16 (2020) no. 1, pp. 46-54 
Nikolay Nessonov. A nonsingular action of the full symmetric group admits an equivalent invariant measure. Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 16 (2020) no. 1, pp. 46-54. http://geodesic.mathdoc.fr/item/JMAG_2020_16_1_a2/
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Voir la notice de l'article provenant de la source Math-Net.Ru

Let $\overline{\mathfrak{S}}_\infty$ denote the set of all bijections of natural numbers. Consider an action of $\overline{\mathfrak{S}}_\infty$ on a measure space $\left( X,\mathfrak{M},\mu \right)$, where $\mu$ is an $\overline{\mathfrak{S}}_\infty$-quasi-invariant measure. We prove that there exists an $\overline{\mathfrak{S}}_\infty$-invariant measure equivalent to $\mu$.

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