Hölder Continuous Derivatives and Ergodic Theory

The purpose of this paper is to prove the existence of an invariant measure for a class of unit interval mappings which have piecewise Hölder derivatives and for which the derivatives are greater than 1 in absolute value. Because of the conclusions of this paper's theorem, results known for a less general class of mappings are seen to be true for the above maps, specifically, the results considering the number of ergodic measures for the mapping, criteria for the Bernoulliness of the “natural” extension, and a central limit theorem.