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A flexible application of the Stone-Weierstrass Theorem in General and Application in Probability Theory Stone-Weierstrass定理在概率论中的灵活应用
Journal of Mathematical Facts and short papers Pub Date : 2019-01-01 DOI: 10.16929/jmfsp/2019.43.006
G. Lo, Lois Chinwendu Okoreke
{"title":"A flexible application of the Stone-Weierstrass Theorem in General and Application in Probability Theory","authors":"G. Lo, Lois Chinwendu Okoreke","doi":"10.16929/jmfsp/2019.43.006","DOIUrl":"https://doi.org/10.16929/jmfsp/2019.43.006","url":null,"abstract":"When applying the classical Stone-Weierstrass common version in Probability Theory for example but in other fields also, some problems may arise if all points of the compact set are not separated. A solution may consist in going back to the proof and finding alternative versions. In this note, we did it and come back with two flexible versions which are easily used for the needs of Probability Theory.","PeriodicalId":210819,"journal":{"name":"Journal of Mathematical Facts and short papers","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124846132","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
On the ubiquitous notion of mean in probability and statistics 论概率统计中普遍存在的均值概念
Journal of Mathematical Facts and short papers Pub Date : 2019-01-01 DOI: 10.16929/jmfsp/2019.35.005
A. Maitournam
{"title":"On the ubiquitous notion of mean in probability and statistics","authors":"A. Maitournam","doi":"10.16929/jmfsp/2019.35.005","DOIUrl":"https://doi.org/10.16929/jmfsp/2019.35.005","url":null,"abstract":"In probability and statistics, the basic notion of probability of an event can be expressed as a mathematical expectation. The latter is a theoretical mean and is an essential parameter of most probability distributions, in particular of the Gaussian distribution. Last but not least, the notion of mean is at the core of two main theorems of probabilities and statistics, that is : the law of large numbers and the central limit theorem. Whether it is a theoretical or empirical version, the concept of mean is omnipresent in probability and statistics, is consubstantial to these two disciplines and is a bridge between randomness and determinism.","PeriodicalId":210819,"journal":{"name":"Journal of Mathematical Facts and short papers","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114282422","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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