Abstract
Let (Ω, ℬ, λ) be a measure space with normalized measure,f:Ω→Ω a nonsingular transformation. We prove: there exists anf-invariant normalized measure which is absolutely continuous with respect to λif and only if there exist δ>0, and α, 0<α<1, such that λ(E)<δ implies λ(f −k(E))<α for allk≧0.
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Communicated by D. Ruelle
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Straube, E. On the existence of invariant, absolutely continuous measures. Commun.Math. Phys. 81, 27–30 (1981). https://doi.org/10.1007/BF01941798
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DOI: https://doi.org/10.1007/BF01941798