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A Category of Probability Spaces
http://hdl.handle.net/2261/00079431
http://hdl.handle.net/2261/00079431203b1130-9cd7-40a4-a8d3-31ad548f8aa2
名前 / ファイル | ライセンス | アクション |
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jms260202.pdf (190.7 kB)
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Item type | 紀要論文 / Departmental Bulletin Paper(1) | |||||
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公開日 | 2020-07-27 | |||||
タイトル | ||||||
タイトル | A Category of Probability Spaces | |||||
言語 | ||||||
言語 | eng | |||||
キーワード | ||||||
主題 | Conditional expectation | |||||
主題Scheme | Other | |||||
キーワード | ||||||
主題 | Radon-Nikodym derivative | |||||
主題Scheme | Other | |||||
キーワード | ||||||
主題 | category theory | |||||
主題Scheme | Other | |||||
資源タイプ | ||||||
資源 | http://purl.org/coar/resource_type/c_6501 | |||||
タイプ | departmental bulletin paper | |||||
著者 |
Adachi, Takanori
× Adachi, Takanori× Ryu, Yoshihiro |
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著者所属 | ||||||
著者所属 | Graduate School of Management, Tokyo Metropolitan University | |||||
著者所属 | ||||||
著者所属 | Department of Mathematical Sciences, Ritsumeikan University | |||||
抄録 | ||||||
内容記述タイプ | Abstract | |||||
内容記述 | We introduce a category $\Prob$ of probability spaces whose objects are all probability spaces and whose arrows correspond to measurable functions satisfying an absolutely continuous requirement. We can consider a $\Prob$-arrow as an evolving direction of information. We introduce a contravariant functor $\mathcal{E}$ from $\Prob$ to $\Set$, the category of sets. The functor $\mathcal{E}$ provides conditional expectations along arrows in $\Prob$, which are generalizations of the classical conditional expectations. For a $\Prob$-arrow $f^-$, we introduce two concepts $f^-$-measurability and $f^-$-independence and investigate their interaction with conditional expectations along $f^-$. We also show that the completion of probability spaces is naturally formulated as an endofunctor of $\Prob$. | |||||
書誌情報 |
Journal of Mathematical Sciences The University of Tokyo 巻 26, 号 2, p. 201-221, 発行日 2019-07-26 |
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ISSN | ||||||
収録物識別子タイプ | ISSN | |||||
収録物識別子 | 13405705 | |||||
書誌レコードID | ||||||
収録物識別子タイプ | NCID | |||||
収録物識別子 | AA11021653 | |||||
Mathmatical Subject Classification | ||||||
60A99(MSC2010) | ||||||
Mathmatical Subject Classification | ||||||
16B50(MSC2010) | ||||||
Mathmatical Subject Classification | ||||||
60G20(MSC2010) | ||||||
Mathmatical Subject Classification | ||||||
18B99(MSC2010) | ||||||
出版者 | ||||||
出版者 | Graduate School of Mathematical Sciences, The University of Tokyo | |||||
原稿受領日 | ||||||
2018-03-19 |