Abstract. The class (IDPFT) of nonsingular infinite direct products T of nonsingular transformations T_n, n∈N, admitting  equivalent invariant probabilities, is studied. If T_n is mildly mixing for all n, the sequence of the Radon-Nikodym derivatives of T_n is asymptotically translation quasi-invariant and T is conservative then the Maharam extension of T is sharply weak mixing. I will discuss some  applications of IDPFT to investigating ergodic properties (weak mixing, Krieger's type, etc.) of nonsingular Gaussian actions (introduced recently by Y.Arano, Y.Isono, A.Marrakchi), nonsingular Poisson actions (introduced recently by E.Roy, Z.Kosloff and myself) and nonsingular Bernoulli shifts.  Joint (2) works: 1) with  M. Leman'czyk, 2) with Z. Kosloff.

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