Mathematical Research Letters

Volume 1, Issue 6, November 1994 pp. 765-768.

A counter example in the Ergodic theory of expanding Markov maps of the interval

Authors: A. G. Abercrombie and R. Nair
Author institution: University of Liverpool

Summary: A theorem popularly called the folklore theorem gives conditions under which an expanding Markov map of the unit interval is known to preserve a measure equivalent to Lebesgue measure, with respect to which it is ergodic and even exact. There is some uncertainty as to how much the hypotheses of this theorem can be weakened. We provide a counter example to one possible strengthening erroneously stated in [Ma].

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