# exactness of the Gauss transformation

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.

-

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.

-
Thank you. I would also like to learn about the others ways to derive this result. For instance, does there exist more elementary ways ? – Steven Neutral Aug 19 '10 at 13:09