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Research for this paper was done, when the first author visited the Institut für mathematische Statistik, Göttingen
The second author was supported by the Deutsche Forschungsgemeinschaft
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Hofbauer, F., Keller, G. Ergodic properties of invariant measures for piecewise monotonic transformations. Math Z 180, 119–140 (1982). https://doi.org/10.1007/BF01215004
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DOI: https://doi.org/10.1007/BF01215004