{"title":"效用函数结构中的具体完备测度","authors":"S. Mohammadzadeh","doi":"10.30495/JME.V0I0.1578","DOIUrl":null,"url":null,"abstract":"An outer measure is constructed on a pseudo-ordered set(X,≿) and then it will be shown that it is in fact a measure defined onthe whole power set of X . Applying this, a measurable utility functionθ is defined which represents the relation ≿ on X. Also, we discuss thecontinuity and upper semi-continuity of θ in certain points of X. Finally,the results are used to improve some of the theorems in economics.","PeriodicalId":43745,"journal":{"name":"Journal of Mathematical Extension","volume":" ","pages":""},"PeriodicalIF":0.4000,"publicationDate":"2021-01-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Specific Complete Measure in the Structure of a Utility Function\",\"authors\":\"S. Mohammadzadeh\",\"doi\":\"10.30495/JME.V0I0.1578\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"An outer measure is constructed on a pseudo-ordered set(X,≿) and then it will be shown that it is in fact a measure defined onthe whole power set of X . Applying this, a measurable utility functionθ is defined which represents the relation ≿ on X. Also, we discuss thecontinuity and upper semi-continuity of θ in certain points of X. Finally,the results are used to improve some of the theorems in economics.\",\"PeriodicalId\":43745,\"journal\":{\"name\":\"Journal of Mathematical Extension\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":0.4000,\"publicationDate\":\"2021-01-11\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Mathematical Extension\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.30495/JME.V0I0.1578\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Mathematical Extension","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.30495/JME.V0I0.1578","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
Specific Complete Measure in the Structure of a Utility Function
An outer measure is constructed on a pseudo-ordered set(X,≿) and then it will be shown that it is in fact a measure defined onthe whole power set of X . Applying this, a measurable utility functionθ is defined which represents the relation ≿ on X. Also, we discuss thecontinuity and upper semi-continuity of θ in certain points of X. Finally,the results are used to improve some of the theorems in economics.
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