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Hausdorff and conformal measures for expanding piecewise monotonic maps of the interval. (English) Zbl 0813.28008
Summary: Let \(A\) be a topologically transitive invariant subset of an expanding piecewise monotonic map on [0,1] with the Darboux property. We investigate existence and uniqueness of conformal measures on \(A\) and relate Hausdorff and conformal measures on \(A\) to each other.

MSC:
28D99 Measure-theoretic ergodic theory
54H20 Topological dynamics (MSC2010)
37A99 Ergodic theory
28D05 Measure-preserving transformations
28A78 Hausdorff and packing measures
Citations:
Zbl 0813.28009
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