Descriptive Estimates for a Set of Points That Approximate an Ergodic Measure
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 generati...
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| Datum: | 2003 |
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| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
Institute of Mathematics, NAS of Ukraine
2003
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/3956 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| Zusammenfassung: | 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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