Some Ergodic Theorems for Piecewise Monotonic Transformations

Let S: w0,1xªw0, 1x be a piecewise monotonic transformation satisfying some conditions. We show that time averages 1rn. njsy01 f(Sj converge strongly in Lp 0, 1.and pointwisely almost everywhere for any fgLp 0, 1., where 1Fp-`.