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Classification of atoms

Azram, Mohammad (2010) Classification of atoms. In: 11th International Pure Mathematical Conference 2010 (IPMC'2010), 6-8 August 2010, Islamabad, Pakistan. (Unpublished)

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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.

Item Type: Conference or Workshop Item (Full Paper)
Additional Information: 3127-2680
Uncontrolled Keywords: Equivalent atoms, σ-field, σ-finite measure, equivalence relation, probability measure, atomic probability space. Mathematics Subject Classification 2000: 60B05
Subjects: Q Science > QA Mathematics
Kulliyyahs/Centres/Divisions/Institutes (Can select more than one option. Press CONTROL button): Kulliyyah of Engineering > Department of Science
Depositing User: Prof Mohammad Azram
Date Deposited: 13 Sep 2011 09:20
Last Modified: 21 Mar 2012 19:18
URI: http://irep.iium.edu.my/id/eprint/2680

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