{"title":"Interior Points of Convex Compact and Continuous Selections of Exact Measures","authors":"Pavel Semenov","doi":"10.1134/S001626632401009X","DOIUrl":null,"url":null,"abstract":"<p> For a metric space <span>\\(M\\)</span>, we prove existence of continuous maps <span>\\(\\{M_n\\}^{\\infty}_{n=1}\\)</span> associating to each compact set <span>\\(K \\subset M\\)</span>, a probability measure <span>\\(M_n(K)\\)</span> with <span>\\(\\operatorname{supp}(M_n(K)) = K\\)</span> in such a way that the set <span>\\(\\{M_n(K)\\}^{\\infty}_{n=1}\\)</span> is dense in the space of probability measures on <span>\\(K\\)</span>. </p>","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":"58 1","pages":"97 - 102"},"PeriodicalIF":0.6000,"publicationDate":"2024-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Functional Analysis and Its Applications","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1134/S001626632401009X","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
For a metric space \(M\), we prove existence of continuous maps \(\{M_n\}^{\infty}_{n=1}\) associating to each compact set \(K \subset M\), a probability measure \(M_n(K)\) with \(\operatorname{supp}(M_n(K)) = K\) in such a way that the set \(\{M_n(K)\}^{\infty}_{n=1}\) is dense in the space of probability measures on \(K\).
期刊介绍:
Functional Analysis and Its Applications publishes current problems of functional analysis, including representation theory, theory of abstract and functional spaces, theory of operators, spectral theory, theory of operator equations, and the theory of normed rings. The journal also covers the most important applications of functional analysis in mathematics, mechanics, and theoretical physics.