Classification of atoms
This article is devoted to give a self-contained presentation of classification of atoms of probability space as equivalent or non-equivalent. It will be established that an event, i.e., a member of a σ-field of a probability space can contains uncountable many equivalent atoms. We will show that th...
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| Format: | Proceeding Paper |
| Language: | English |
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2010
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| Online Access: | http://irep.iium.edu.my/2680/1/CLASSIFICATION_OF_ATOMS.pdf |
| _version_ | 1825644336241442816 |
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| author | Azram, Mohammad |
| author_facet | Azram, Mohammad |
| author_sort | Azram, Mohammad |
| collection | IIUM |
| description | This article is devoted to give a self-contained presentation of classification of atoms of probability space as equivalent or non-equivalent. It will be established that an event, i.e., a member of a σ-field of a probability space can contains uncountable many equivalent atoms. We will show that the relation of being equivalent atoms is an equivalence relation. An independent proof will enable us to state that an event of a probability space with σ-finite probability measure can contains at most countable many non-equivalent atoms. We will also establish that for a purely atomic probability space with σ-finite probability measure, probability measure of every event is equal to the sum of the probability measures of its non-equivalent atoms. We will also justify that in some of the results, the probability space and respective probability measure can be replaced as measure space and respective measure. |
| first_indexed | 2024-03-05T22:31:20Z |
| format | Proceeding Paper |
| id | oai:generic.eprints.org:2680 |
| institution | International Islamic University Malaysia |
| language | English |
| last_indexed | 2024-03-05T22:31:20Z |
| publishDate | 2010 |
| record_format | dspace |
| spelling | oai:generic.eprints.org:26802012-03-21T11:18:17Z http://irep.iium.edu.my/2680/ Classification of atoms Azram, Mohammad QA Mathematics This article is devoted to give a self-contained presentation of classification of atoms of probability space as equivalent or non-equivalent. It will be established that an event, i.e., a member of a σ-field of a probability space can contains uncountable many equivalent atoms. We will show that the relation of being equivalent atoms is an equivalence relation. An independent proof will enable us to state that an event of a probability space with σ-finite probability measure can contains at most countable many non-equivalent atoms. We will also establish that for a purely atomic probability space with σ-finite probability measure, probability measure of every event is equal to the sum of the probability measures of its non-equivalent atoms. We will also justify that in some of the results, the probability space and respective probability measure can be replaced as measure space and respective measure. 2010 Proceeding Paper NonPeerReviewed application/pdf en http://irep.iium.edu.my/2680/1/CLASSIFICATION_OF_ATOMS.pdf Azram, Mohammad (2010) Classification of atoms. In: 11th International Pure Mathematical Conference 2010 (IPMC'2010), 6-8 August 2010, Islamabad, Pakistan. (Unpublished) http://www.austms.org.au/tiki-calendar.php?editmode=details&calitemId=213 |
| spellingShingle | QA Mathematics Azram, Mohammad Classification of atoms |
| title | Classification of atoms |
| title_full | Classification of atoms |
| title_fullStr | Classification of atoms |
| title_full_unstemmed | Classification of atoms |
| title_short | Classification of atoms |
| title_sort | classification of atoms |
| topic | QA Mathematics |
| url | http://irep.iium.edu.my/2680/1/CLASSIFICATION_OF_ATOMS.pdf |
| work_keys_str_mv | AT azrammohammad classificationofatoms |