On the existence of invariant, absolutely continuous measures
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Let (, , ) be a measure space with normalized measure, f: a nonsingular transformation. We prove: there exists an f-invariant normalized measure which is absolutely continuous with respect to if and only if there exist >0, and , 0<<1, such that (E)< implies (f-k(E))< for all k0. 1981 Springer-Verlag.
Communications in Mathematical Physics
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