{"title":"A generalization of duality theorem in the theory of linear programming","authors":"M. Ohtsuka","doi":"10.32917/HMJ/1206139186","DOIUrl":null,"url":null,"abstract":"The well-known duality theorem in the theory of linear programming asserts that, if Jίφ0 and M<oo, then Jί'Φtf and M=M'. We shall generalize this theorem in the present paper. Let X and Y be compact Hausdorff spaces and Φ(x, γ) a universally measurable function on XxY which is bounded below. Let g(χ) be a universally measurable function on X which is bounded below and /(γ) a universally measurable function on Y which is bounded above. Under these general circumstances let Jί be the class of all non-negative Radon measures μ on Y satisfying","PeriodicalId":17080,"journal":{"name":"Journal of science of the Hiroshima University Ser. A Mathematics, physics, chemistry","volume":"47 1","pages":"31-39"},"PeriodicalIF":0.0000,"publicationDate":"1966-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"11","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of science of the Hiroshima University Ser. A Mathematics, physics, chemistry","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.32917/HMJ/1206139186","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 11
Abstract
The well-known duality theorem in the theory of linear programming asserts that, if Jίφ0 and M