On a Class of Transformations which have Unique Absolutely Continuous Invariant Measures
- 1 November 1979
- journal article
- Published by JSTOR in Transactions of the American Mathematical Society
- Vol. 255, 243-262
- https://doi.org/10.2307/1998174
Abstract
A class of piecewise transformations from an interval into itself with slopes greater than 1 in absolute value, and having the property that it takes partition points into partition points is shown to have unique absolutely continuous invariant measures. For this class of functions, a central limit theorem holds for all real measurable functions. For the subclass of piecewise linear transformations having a fixed point, it is shown that the unique absolutely continuous invariant measures are piecewise constant.Keywords
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