A generalization of a result of R. Lyons about measures on [0, 1) |
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Authors: | J Feldman |
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Institution: | (1) Department of Mathematics, University of California at Berkeley, 94720 Berkeley, California, USA |
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Abstract: | Letμ be a probability measure on 0, 1), invariant underS:x ↦px mod 1, and for which almost every ergodic component has positive entropy. Ifq is a real number greater than 1 for which logq/ logp is irrational, andT
n sendsx toq
nx mod 1, then for any ε>0 the measureμT
n
−1
will — for a set ofn of positive lower density — be within ε of Lebesgue measure. |
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Keywords: | |
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