{"title":"积分度量空间的有限维切比雪夫子空间","authors":"N. K. Rakhmetov","doi":"10.1070/SM1993V074N02ABEH003351","DOIUrl":null,"url":null,"abstract":"This is a detailed study of the problem of the existence and characterization of finite-dimensional Chebyshev subspaces of the spaces and on the interval , where is an even nonnegative continuous nondecreasing function on the half-line , and the function is measurable, finite, and positive almost everywhere on . If is an -function, it is characterized as a Chebyshev subspace of the Orlicz spaces with the Luxemburg norm.","PeriodicalId":208776,"journal":{"name":"Mathematics of The Ussr-sbornik","volume":"30 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1993-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"ON FINITE-DIMENSIONAL CHEBYSHEV SUBSPACES OF SPACES WITH AN INTEGRAL METRIC\",\"authors\":\"N. K. Rakhmetov\",\"doi\":\"10.1070/SM1993V074N02ABEH003351\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"This is a detailed study of the problem of the existence and characterization of finite-dimensional Chebyshev subspaces of the spaces and on the interval , where is an even nonnegative continuous nondecreasing function on the half-line , and the function is measurable, finite, and positive almost everywhere on . If is an -function, it is characterized as a Chebyshev subspace of the Orlicz spaces with the Luxemburg norm.\",\"PeriodicalId\":208776,\"journal\":{\"name\":\"Mathematics of The Ussr-sbornik\",\"volume\":\"30 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1993-02-28\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mathematics of The Ussr-sbornik\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1070/SM1993V074N02ABEH003351\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematics of The Ussr-sbornik","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1070/SM1993V074N02ABEH003351","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
ON FINITE-DIMENSIONAL CHEBYSHEV SUBSPACES OF SPACES WITH AN INTEGRAL METRIC
This is a detailed study of the problem of the existence and characterization of finite-dimensional Chebyshev subspaces of the spaces and on the interval , where is an even nonnegative continuous nondecreasing function on the half-line , and the function is measurable, finite, and positive almost everywhere on . If is an -function, it is characterized as a Chebyshev subspace of the Orlicz spaces with the Luxemburg norm.
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