Nonsingular Poisson Suspensions

The classical Poisson functor associates to every infinite measure preserving dynamical system (X, μ, T) a probability (X*, μ*, T*) called the suspension of T. In this paper we generalize construction: subgroup Aut2(X, μ) μ-nonsingular transformations T X is specified as largest for which T* μ*-nonsingular. topological structure studied. We show that generic element in ergodic and Krieger type III1. Let G be locally compact Polish group let A: → G-action. investigate properties A* A terms an affine representation associated naturally with A. It shown has property (T), if only each nonsingular G-action admits absolutely continuous invariant probability. If does not have then generating κ on t > 0, constructed whose Furstenberg κ-entropy t.