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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Main Author: Azram, Mohammad
Format: Proceeding Paper
Language:English
Published: 2010
Subjects:
Online Access:http://irep.iium.edu.my/2680/1/CLASSIFICATION_OF_ATOMS.pdf
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author Azram, Mohammad
author_facet Azram, Mohammad
author_sort Azram, Mohammad
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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.
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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