TITLE: Rohklin’s formula and $\beta$ expansions
QUESTION [6 upvotes]: I've been reading K. Dajani and C. Kraaikamp's paper From greedy to lazy expansions and their driving dynamics. In the last page previous to the references, they mention that the entropy of the map $T_{\alpha, \beta}(x) = \beta x + \alpha$ is $\log(\beta)$. They mention this fact follows from the Rohklin’s formula for calculating the entropy. What I would like to know is a reference where this formula is stated and proved.
Thanks a lot in advance.

REPLY [5 votes]: This is the formula 
$$
h_\mu(f) = \int \log |f'|\,d\mu
$$
for the entropy of an absolutely continuous $f$-invariant measure $\mu$ on the unit interval which goes back to Rokhlin (http://www.ams.org/mathscinet-getitem?mr=143873), also see Ledrappier (http://www.ams.org/mathscinet-getitem?mr=627788).