{"title":"可测量的光谱分解","authors":"Bomi Shin","doi":"10.1007/s00605-024-01961-3","DOIUrl":null,"url":null,"abstract":"<p>introduce the spectral decomposition property for measures and prove that a homeomorphism has the spectral decomposition property if and only if every Borel probability measure has the property too. Furthermore, we show that all shadowable measures for expansive homeomorphisms have the spectral decomposition property. Additionally, we provide illustrative examples relevant to these results.</p>","PeriodicalId":18913,"journal":{"name":"Monatshefte für Mathematik","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2024-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A measurable spectral decomposition\",\"authors\":\"Bomi Shin\",\"doi\":\"10.1007/s00605-024-01961-3\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>introduce the spectral decomposition property for measures and prove that a homeomorphism has the spectral decomposition property if and only if every Borel probability measure has the property too. Furthermore, we show that all shadowable measures for expansive homeomorphisms have the spectral decomposition property. Additionally, we provide illustrative examples relevant to these results.</p>\",\"PeriodicalId\":18913,\"journal\":{\"name\":\"Monatshefte für Mathematik\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-04-05\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Monatshefte für Mathematik\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1007/s00605-024-01961-3\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Monatshefte für Mathematik","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1007/s00605-024-01961-3","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
introduce the spectral decomposition property for measures and prove that a homeomorphism has the spectral decomposition property if and only if every Borel probability measure has the property too. Furthermore, we show that all shadowable measures for expansive homeomorphisms have the spectral decomposition property. Additionally, we provide illustrative examples relevant to these results.
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