Abstract
We obtain descriptive estimates for a set of points that approximate an ergodic invariant measure of a continuous mapping on a compact set. For example, in the case of a metrically transitive mapping with an invariant measure equivalent to the Lebesgue measure, we prove that a set of points generating invariant measures with maximum support contains a dense G δ-set, whereas, in the general case, one has a much worse estimate G δσδ.
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Sivak, A.G. Descriptive Estimates for a Set of Points That Approximate an Ergodic Measure. Ukrainian Mathematical Journal 55, 987–992 (2003). https://doi.org/10.1023/B:UKMA.0000010598.85572.5b
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DOI: https://doi.org/10.1023/B:UKMA.0000010598.85572.5b