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Hybrid ·Peer-reviewed·ISSN (Online): 2169-012X·ISSN (Print): 0972-0502

Monthly Journal: Publishes the methodological and theoretical role of mathematics and mathematical applications underpinning scientific research.

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Open Access Research Article

Common extension of two sigma-finite measures

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pp. 527–534Vol. 27Issue 3April 2024DOI: 10.47974/JIM-1742XML
Received:
08 Mar 2023
Published Online:
07 May 2024
Article type:
Research Article
Language:
EN
Article no.:
JIM-1742
Pages:
527–534

Abstract

A σ – finite measure is obtained as the unique common extension of two σ – finite measures defined on two disjoint rings.  This is done by first considering an outer measure on a σ – ring containing both disjoint rings.  This outer measure then gives rise to the unique extension in question.

Keywords

Subject Classifications

28A1228A05

References

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[3] H. Halmos, Measure Theory, Springer-Verlag, New York (1974).
[4] A. Kharazishvili, Topics in Measure Theory and Real Analysis: The Measure Extension Problem and  Related Questions (Atlantis Studies in Mathematics), Atlantic Press, Amsterdam-Paris (2009).
[5] M. Sahin, N. Olgun, F. Akyildiz and A. Karakus, Generalized Caratheodory extension theorem on  fuzzy measure space, Abstract and Applied Analysis, Vol. 2012, Article ID 260457, 11  pages (2012).
[6] N. Sookoo, Extension of measures on two disjoint rings, Journal of Interdisciplinary Mathematics,  Vol. 21, Issue 6, 1447-1456 (2018). 

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