Generic nonsingular Poisson suspension is of type $III_1$

Alexandre I. Danilenko, Zemer Kosloff, Emmanuel Roy

Published 2020-02-12Version 1

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 $III_1$.