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We apply the (C, F)-construction from [Da] to produce a number of funny rank one infinite measure preserving actions of Abelian groups G with " unusual " multiple recurrence properties. In particular, we construct the following for each p ∈ N ∪ {∞}: (i) a p-recurrent action T = (T g) g∈G such that (if p = ∞) no one transformation T g is (p + 1)-recurrent(More)
We introduce high staircase infinite measure preserving transformations and prove that they are mixing under a restricted growth condition. This is used to (i) realize each subset E ⊂ N as the set of essential values of the multiplicity function for the Koopman operator of a mixing ergodic infinite measure preserving transformation, (ii) construct mixing(More)
Let X and Y be Polish spaces with non-atomic Borel measures µ and ν of full support. Suppose that T and S are ergodic non-singular homeomorphisms of (X, µ) and (Y, ν) with continuous Radon-Nikodym derivatives. Suppose that either they are both of type III 1 or that they are both of type III λ , 0 < λ < 1 and, in the III λ case, suppose in addition that both(More)
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