Generic non-singular Poisson suspension is of type III1

Abstract

\n It is shown that for a dense \n \n \n $G_\\delta $\n \n -subset of the subgroup of non-singular transformations (of a standard infinite \n \n \n $\\sigma $\n \n -finite measure space) whose Poisson suspensions are non-singular, the corresponding Poisson suspensions are ergodic and of Krieger’s type\xa0III1.