Classification of atoms

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...

Full description

Bibliographic Details
Main Authors: Azram, Mohammad, Elfaki, Faiz Ahmed Mohamed, Daoud, Jamal Ibrahim
Format: Article
Language:English
Published: INSI Publications 2011
Subjects:
QC Physics
Online Access:http://irep.iium.edu.my/3734/
http://irep.iium.edu.my/3734/
http://irep.iium.edu.my/3734/1/Jamal-9.pdf
id iium-3734
recordtype eprints
spelling iium-37342012-02-09T02:08:44Z http://irep.iium.edu.my/3734/ Classification of atoms Azram, Mohammad Elfaki, Faiz Ahmed Mohamed Daoud, Jamal Ibrahim QC Physics 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. INSI Publications 2011 Article PeerReviewed application/pdf en http://irep.iium.edu.my/3734/1/Jamal-9.pdf 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 http://www.insipub.com/ajbas_may_2011.html
repository_type Digital Repository
institution_category Local University
institution International Islamic University Malaysia
building IIUM Repository
collection Online Access
language English
topic QC Physics
spellingShingle QC Physics
Azram, Mohammad
Elfaki, Faiz Ahmed Mohamed
Daoud, Jamal Ibrahim
Classification of atoms
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.
format Article
author Azram, Mohammad
Elfaki, Faiz Ahmed Mohamed
Daoud, Jamal Ibrahim
author_facet Azram, Mohammad
Elfaki, Faiz Ahmed Mohamed
Daoud, Jamal Ibrahim
author_sort Azram, Mohammad
title Classification of atoms
title_short Classification of atoms
title_full Classification of atoms
title_fullStr Classification of atoms
title_full_unstemmed Classification of atoms
title_sort classification of atoms
publisher INSI Publications
publishDate 2011
url http://irep.iium.edu.my/3734/
http://irep.iium.edu.my/3734/
http://irep.iium.edu.my/3734/1/Jamal-9.pdf
first_indexed 2023-09-18T20:11:41Z
last_indexed 2023-09-18T20:11:41Z
_version_ 1777407519666208768

Similar Items