Computing invariant measures of piecewise convex transformations

LetS:[0, 1][0,1] be a piecewise convex transformation satisfying some conditions which guarantee the existence of an absolutely continuous invariant probability measure. We prove the convergence of a class of Markov finite approximations for computing the invariant measure, using a compactness argument forL¹-spaces.Research was supported in part by a grant from the Minority Scholars Program through the University of Southern Mississippi.