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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| Date: | 2003 |
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| Main Authors: | , |
| Format: | Article |
| Language: | English |
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Institute of Mathematics, NAS of Ukraine
2003
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/3956 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860510080895549440 |
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| author | Sivak, A. G. Сивак, А. Г. Сивак, А. Г. |
| author_facet | Sivak, A. G. Сивак, А. Г. Сивак, А. Г. |
| author_sort | Sivak, A. G. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-18T20:16:01Z |
| description | 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. |
| first_indexed | 2026-03-24T02:51:19Z |
| format | Article |
| fulltext | |
| id | umjimathkievua-article-3956 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | English |
| last_indexed | 2026-03-24T02:51:19Z |
| publishDate | 2003 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
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| spelling | umjimathkievua-article-39562020-03-18T20:16:01Z Descriptive Estimates for a Set of Points That Approximate an Ergodic Measure Дескриптивные оценки множества точек, аппроксимирующих эргодическую меру Sivak, A. G. Сивак, А. Г. Сивак, А. Г. 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. Отримано дескриптивні оцінки множини точок, що апроксимуіоть ергодичну інваріантну міру неперервного відображення на компакті. Доведено, наприклад, що для метрично транзитивного відображення з інваріантною мірою, еквівалентною мірі Лебега, множина точок, які породжують інваріантні міри з максимальним носієм, містить щільну $Gδ$-множину, тоді як у загальному випадку мас місце значно гірша оцінка $δσδ$. Institute of Mathematics, NAS of Ukraine 2003-06-25 Article Article https://umj.imath.kiev.ua/index.php/umj/article/view/3956 Ukrains’kyi Matematychnyi Zhurnal; Vol. 55 No. 6 (2003); 817-823 Український математичний журнал; Том 55 № 6 (2003); 817-823 1027-3190 en https://umj.imath.kiev.ua/index.php/umj/article/view/3956/4625 Copyright (c) 2003 Sivak A. G. |
| spellingShingle | Sivak, A. G. Сивак, А. Г. Сивак, А. Г. Descriptive Estimates for a Set of Points That Approximate an Ergodic Measure |
| title | Descriptive Estimates for a Set of Points That Approximate an Ergodic Measure |
| title_alt | Дескриптивные оценки множества точек, аппроксимирующих эргодическую меру |
| title_full | Descriptive Estimates for a Set of Points That Approximate an Ergodic Measure |
| title_fullStr | Descriptive Estimates for a Set of Points That Approximate an Ergodic Measure |
| title_full_unstemmed | Descriptive Estimates for a Set of Points That Approximate an Ergodic Measure |
| title_short | Descriptive Estimates for a Set of Points That Approximate an Ergodic Measure |
| title_sort | descriptive estimates for a set of points that approximate an ergodic measure |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/3956 |
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