{"title":"P(K) 空间拓扑特性概览","authors":"Grzegorz Plebanek","doi":"10.1007/s11537-024-2410-y","DOIUrl":null,"url":null,"abstract":"<p>Given a compact space <i>K</i>, we denote by <i>P</i>(<i>K</i>) the space of all Radon probability measures on <i>K</i>, equipped with the <i>weak*</i> topology inherited from <i>C</i>(<i>K</i>)*. For nonmetrizable compacta <i>K</i> even basic properties of <i>P</i>(<i>K</i>) spaces depend of additional axioms of set theory. We discuss here older and quite recent results on the subject.</p>","PeriodicalId":54908,"journal":{"name":"Japanese Journal of Mathematics","volume":"38 1","pages":""},"PeriodicalIF":1.8000,"publicationDate":"2024-08-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A survey on topological properties of P(K) spaces\",\"authors\":\"Grzegorz Plebanek\",\"doi\":\"10.1007/s11537-024-2410-y\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>Given a compact space <i>K</i>, we denote by <i>P</i>(<i>K</i>) the space of all Radon probability measures on <i>K</i>, equipped with the <i>weak*</i> topology inherited from <i>C</i>(<i>K</i>)*. For nonmetrizable compacta <i>K</i> even basic properties of <i>P</i>(<i>K</i>) spaces depend of additional axioms of set theory. We discuss here older and quite recent results on the subject.</p>\",\"PeriodicalId\":54908,\"journal\":{\"name\":\"Japanese Journal of Mathematics\",\"volume\":\"38 1\",\"pages\":\"\"},\"PeriodicalIF\":1.8000,\"publicationDate\":\"2024-08-29\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Japanese Journal of Mathematics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s11537-024-2410-y\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Japanese Journal of Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s11537-024-2410-y","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
Given a compact space K, we denote by P(K) the space of all Radon probability measures on K, equipped with the weak* topology inherited from C(K)*. For nonmetrizable compacta K even basic properties of P(K) spaces depend of additional axioms of set theory. We discuss here older and quite recent results on the subject.
期刊介绍：
The official journal of the Mathematical Society of Japan, the Japanese Journal of Mathematics is devoted to authoritative research survey articles that will promote future progress in mathematics. It encourages advanced and clear expositions, giving new insights on topics of current interest from broad perspectives and/or reviewing all major developments in an important area over many years.
An eminent international mathematics journal, the Japanese Journal of Mathematics has been published since 1924. It is an ideal resource for a wide range of mathematicians extending beyond a small circle of specialists.
The official journal of the Mathematical Society of Japan.
Devoted to authoritative research survey articles that will promote future progress in mathematics.
Gives new insight on topics of current interest from broad perspectives and/or reviews all major developments in an important area over many years.
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