{"title":"形式化哈尔测度","authors":"Floris van Doorn","doi":"10.4230/LIPIcs.ITP.2021.18","DOIUrl":null,"url":null,"abstract":"We describe the formalization of the existence and uniqueness of Haar measure in the Lean theorem prover. The Haar measure is an invariant regular measure on locally compact groups, and it has not been formalized in a proof assistant before. We will also discuss the measure theory library in Lean's mathematical library \\textsf{mathlib}, and discuss the construction of product measures and the proof of Fubini's theorem for the Bochner integral.","PeriodicalId":296683,"journal":{"name":"International Conference on Interactive Theorem Proving","volume":"23 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2021-02-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"9","resultStr":"{\"title\":\"Formalized Haar Measure\",\"authors\":\"Floris van Doorn\",\"doi\":\"10.4230/LIPIcs.ITP.2021.18\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We describe the formalization of the existence and uniqueness of Haar measure in the Lean theorem prover. The Haar measure is an invariant regular measure on locally compact groups, and it has not been formalized in a proof assistant before. We will also discuss the measure theory library in Lean's mathematical library \\\\textsf{mathlib}, and discuss the construction of product measures and the proof of Fubini's theorem for the Bochner integral.\",\"PeriodicalId\":296683,\"journal\":{\"name\":\"International Conference on Interactive Theorem Proving\",\"volume\":\"23 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2021-02-04\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"9\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"International Conference on Interactive Theorem Proving\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.4230/LIPIcs.ITP.2021.18\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Conference on Interactive Theorem Proving","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.4230/LIPIcs.ITP.2021.18","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
We describe the formalization of the existence and uniqueness of Haar measure in the Lean theorem prover. The Haar measure is an invariant regular measure on locally compact groups, and it has not been formalized in a proof assistant before. We will also discuss the measure theory library in Lean's mathematical library \textsf{mathlib}, and discuss the construction of product measures and the proof of Fubini's theorem for the Bochner integral.
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