Generic nonsingular Poisson suspension is of type $III_1$

Published 12 Feb 2020 in math.DS | (2002.05094v1)

Abstract: It is shown that for a dense $G_\delta$-subset of the subgroup of nonsingular transformations (of a standard infinite $\sigma$-finite measure space) whose Poisson suspensions are nonsingular, the corresponding Poisson suspensions are ergodic and of Krieger's type $III_1$.

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