Abstract
Under certain conditions a many-to-one transformation of the unit interval onto itself possesses a finite invariant ergodic measure equivalent to Lebesgue measure. The purpose of this paper is to investigate these conditions and to show how differentiable and analytic properties of the invariant density are inherited from the original transformation.
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Halfant, M. Analytic properties of Rényi’s invariant density. Israel J. Math. 27, 1–20 (1977). https://doi.org/10.1007/BF02761603
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DOI: https://doi.org/10.1007/BF02761603