Mathematical Research Letters

Volume 1 (1994)

Number 6

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

Pages: 765 – 768



R. Nair (University of Liverpool)

A. G. University of Liverpool (University of Liverpool)


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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