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Orthogonal vector measures

Orthogonal vector measures This paper introduces the concept of orthogonal vector measures, and gives the Yosida-Hewitt decomposition theorem for this kind of vector measures. The major results are (a) Any orthogonal vector measure can gain it countable additivity by enlarging its domain; (b) Every orthogonal vector measure can be represented as the sum of two orthogonal vector measures, one of which is countably additive, and the other is purely finitely additive. Furthermore, these vector measures are completely perpendicular to each other. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Mathematicae Applicatae Sinica Springer Journals

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Publisher
Springer Journals
Copyright
Copyright © 1990 by Science Press, Beijing, China and Allerton Press, Inc., New York, U.S.A.
Subject
Mathematics; Applications of Mathematics; Math Applications in Computer Science; Theoretical, Mathematical and Computational Physics
ISSN
0168-9673
eISSN
1618-3932
DOI
10.1007/BF02014719
Publisher site
See Article on Publisher Site

Abstract

This paper introduces the concept of orthogonal vector measures, and gives the Yosida-Hewitt decomposition theorem for this kind of vector measures. The major results are (a) Any orthogonal vector measure can gain it countable additivity by enlarging its domain; (b) Every orthogonal vector measure can be represented as the sum of two orthogonal vector measures, one of which is countably additive, and the other is purely finitely additive. Furthermore, these vector measures are completely perpendicular to each other.

Journal

Acta Mathematicae Applicatae SinicaSpringer Journals

Published: Jul 15, 2005

References