Abstract

We consider a transformation T of the unit interval (0, 1) into itself which is piecewise $C\sp2$ and expanding. Using the spectral decomposition of the Frobenius-Perron operator of T, we give a proof of the Central Limit Theorem for$$\left({1\over n}\right)\sum\sbsp{i=0}{n-1}f\circ T\sp{i},$$where f is a function of bounded variation. It is also shown that the speed of covergence in the Central Limit Theorem is of the order ${1\over\sqrt n}.$