I've been reading K. Dajani and C. Kraaikamp's paper [From greedy to lazy expansions and their driving dynamics](http://dutiosc.twi.tudelft.nl/~cork/monthly.pdf). 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. 



Rohklin’s formula and $\beta$ expansions
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>).


