Classification of atoms

Azram, Mohammad and Elfaki, Faiz Ahmed Mohamed and Daoud, Jamal Ibrahim (2011) Classification of atoms. Australian Journal of Basic and Applied Sciences, 5 (5). pp. 5-8. ISSN 1991-8178

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Abstract

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:	Article (Journal)
Additional Information:	3127/3734
Uncontrolled Keywords:	Equivalent atoms, σ-field, σ-finite measure, equivalence relation, probability measure, atomic probability space
Subjects:	Q Science > QC Physics
Kulliyyahs/Centres/Divisions/Institutes (Can select more than one option. Press CONTROL button):	Kulliyyah of Engineering > Department of Science
Depositing User:	Assoc.Prof.Dr Jamal Daoud
Date Deposited:	21 Sep 2011 12:18
Last Modified:	09 Feb 2012 10:08
URI:	http://irep.iium.edu.my/id/eprint/3734

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