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Dear all,

I would like to know if the Gauss transformation T(x) = fractional part of 1/x, x in (0,1) (with the Gauss invariant probability measure) is an exact endomorphism (in the sense of Rokhlin). I have failed to find an answer in the literature, any reference would be welcomed.

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Hi Steven,

the answer to your question is yes and there are several ways of deriving the exactness of Gauss map with respect to Gauss probability: for instance, in this text of M. Viana, it is derived as a consequence of the proof of the exponential decay of correlations.

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  • $\begingroup$ Thank you. I would also like to learn about the others ways to derive this result. For instance, does there exist more elementary ways ? $\endgroup$ Aug 19, 2010 at 13:09

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