{"title":"多极集上的四元蒙日-安培测度","authors":"Hichame Amal, Saïd Asserda, Fadoua Boukhari","doi":"10.1007/s10114-024-2227-x","DOIUrl":null,"url":null,"abstract":"<div><p>In this paper, we prove that in a hyperconvex domain Ω in ℍ<sup><i>n</i></sup>, if a non-negative Borel measure is dominated by a quaternionic Monge–Ampère measure, then it is a quaternionic Monge–Ampère measure of a function in the class <span>\\({\\cal E}(\\Omega )\\)</span>.</p></div>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-02-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Quaternionic Monge–Ampère Measure on Pluripolar Set\",\"authors\":\"Hichame Amal, Saïd Asserda, Fadoua Boukhari\",\"doi\":\"10.1007/s10114-024-2227-x\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>In this paper, we prove that in a hyperconvex domain Ω in ℍ<sup><i>n</i></sup>, if a non-negative Borel measure is dominated by a quaternionic Monge–Ampère measure, then it is a quaternionic Monge–Ampère measure of a function in the class <span>\\\\({\\\\cal E}(\\\\Omega )\\\\)</span>.</p></div>\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2024-02-02\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s10114-024-2227-x\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s10114-024-2227-x","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Quaternionic Monge–Ampère Measure on Pluripolar Set
In this paper, we prove that in a hyperconvex domain Ω in ℍn, if a non-negative Borel measure is dominated by a quaternionic Monge–Ampère measure, then it is a quaternionic Monge–Ampère measure of a function in the class \({\cal E}(\Omega )\).
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