{"created":"2021-03-01T07:15:58.859648+00:00","id":54315,"links":{},"metadata":{"_buckets":{"deposit":"4b0cd2e5-4c64-46f4-876c-88e3476cef31"},"_deposit":{"id":"54315","owners":[],"pid":{"revision_id":0,"type":"depid","value":"54315"},"status":"published"},"_oai":{"id":"oai:repository.dl.itc.u-tokyo.ac.jp:00054315","sets":["312:6865:8351:8436","9:504:6868:8353:8437"]},"item_4_biblio_info_7":{"attribute_name":"書誌情報","attribute_value_mlt":[{"bibliographicIssueDates":{"bibliographicIssueDate":"2019-07-26","bibliographicIssueDateType":"Issued"},"bibliographicIssueNumber":"2","bibliographicPageEnd":"221","bibliographicPageStart":"201","bibliographicVolumeNumber":"26","bibliographic_titles":[{"bibliographic_title":"Journal of Mathematical Sciences The University of Tokyo"}]}]},"item_4_description_5":{"attribute_name":"抄録","attribute_value_mlt":[{"subitem_description":"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 $\\Prob$.","subitem_description_type":"Abstract"}]},"item_4_publisher_20":{"attribute_name":"出版者","attribute_value_mlt":[{"subitem_publisher":"Graduate School of Mathematical Sciences, The University of Tokyo"}]},"item_4_source_id_10":{"attribute_name":"書誌レコードID","attribute_value_mlt":[{"subitem_source_identifier":"AA11021653","subitem_source_identifier_type":"NCID"}]},"item_4_source_id_8":{"attribute_name":"ISSN","attribute_value_mlt":[{"subitem_source_identifier":"13405705","subitem_source_identifier_type":"ISSN"}]},"item_4_text_17":{"attribute_name":"Mathmatical Subject Classification","attribute_value_mlt":[{"subitem_text_value":"60A99(MSC2010)"},{"subitem_text_value":"16B50(MSC2010)"},{"subitem_text_value":"60G20(MSC2010)"},{"subitem_text_value":"18B99(MSC2010)"}]},"item_4_text_33":{"attribute_name":"原稿受領日","attribute_value_mlt":[{"subitem_text_value":"2018-03-19"}]},"item_4_text_4":{"attribute_name":"著者所属","attribute_value_mlt":[{"subitem_text_value":"Graduate School of Management, Tokyo Metropolitan University"},{"subitem_text_value":"Department of Mathematical Sciences, Ritsumeikan University"}]},"item_creator":{"attribute_name":"著者","attribute_type":"creator","attribute_value_mlt":[{"creatorNames":[{"creatorName":"Adachi, Takanori"}],"nameIdentifiers":[{"nameIdentifier":"161519","nameIdentifierScheme":"WEKO"}]},{"creatorNames":[{"creatorName":"Ryu, Yoshihiro"}],"nameIdentifiers":[{"nameIdentifier":"161520","nameIdentifierScheme":"WEKO"}]}]},"item_files":{"attribute_name":"ファイル情報","attribute_type":"file","attribute_value_mlt":[{"accessrole":"open_date","date":[{"dateType":"Available","dateValue":"2020-07-27"}],"displaytype":"detail","filename":"jms260202.pdf","filesize":[{"value":"190.7 kB"}],"format":"application/pdf","licensetype":"license_note","mimetype":"application/pdf","url":{"label":"jms260202.pdf","url":"https://repository.dl.itc.u-tokyo.ac.jp/record/54315/files/jms260202.pdf"},"version_id":"918aea5f-4a53-42e7-bbc5-70950b2c96c4"}]},"item_keyword":{"attribute_name":"キーワード","attribute_value_mlt":[{"subitem_subject":"Conditional expectation","subitem_subject_scheme":"Other"},{"subitem_subject":"Radon-Nikodym derivative","subitem_subject_scheme":"Other"},{"subitem_subject":"category theory","subitem_subject_scheme":"Other"}]},"item_language":{"attribute_name":"言語","attribute_value_mlt":[{"subitem_language":"eng"}]},"item_resource_type":{"attribute_name":"資源タイプ","attribute_value_mlt":[{"resourcetype":"departmental bulletin paper","resourceuri":"http://purl.org/coar/resource_type/c_6501"}]},"item_title":"A Category of Probability Spaces","item_titles":{"attribute_name":"タイトル","attribute_value_mlt":[{"subitem_title":"A Category of Probability Spaces"}]},"item_type_id":"4","owner":"1","path":["8436","8437"],"pubdate":{"attribute_name":"公開日","attribute_value":"2020-07-27"},"publish_date":"2020-07-27","publish_status":"0","recid":"54315","relation_version_is_last":true,"title":["A Category of Probability Spaces"],"weko_creator_id":"1","weko_shared_id":null},"updated":"2022-12-19T04:31:50.653177+00:00"}