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Existence of nonatomic charges

Part of: Classical measure theory

Published online by Cambridge University Press:  09 April 2009

K. P. S. Bhaskara Rao  and
M. Bhaskara Rao
K. P. S. Bhaskara Rao
Affiliation:
Mathematical Statistics Indian Statistical InstituteCalcuttaIndia
M. Bhaskara Rao
Affiliation:
Department of Probability and Statistics The University of SheffieldSheffieldU.K.
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Abstract

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A complete characterization of Boolean algebras which admit nonatomic charges (i.e. finitely additive measures) is obtained. This also gives rise to a characterization of superatomic Boolean algebras. We also consider the problem of denseness of the set of all nonatomic charges in the space of all charges on a given Boolean algebra, equipped with a suitable topology.

MSC classification

Secondary: 28A60: Measures on Boolean rings, measure algebras
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 25 , Issue 1 , February 1978 , pp. 1 - 6
Copyright
Copyright © Australian Mathematical Society 1978

References

Berberian, S. K. (1962), Measure and Integration (Macmillan, New York).Google Scholar
Halmos, P. R. (1950), Measure Theory (Van Nostrand, New York).CrossRefGoogle Scholar
Halmos, P. R. (1963), Lectures on Boolean Algebras (Van Nostrand, New York).Google Scholar
Knowles, J. D. (1967), On the existence of nonatomic measures, Mathematika 14, 62–67.CrossRefGoogle Scholar
Kuratowski, K. (1966), Topology 1 (Academic Press, New York).Google Scholar
Luther, N. Y. (1970), “Weak denseness of nonatomic measures on perfect, locally compact spaces”, Pacific J. of Math. 34, 453–460.CrossRefGoogle Scholar
Pierce, R. S. (1970), “Existence and uniqueness theorems for extensions of zero-dimensional compact metric spaces”, Trans. Amer. Math. Soc. 148, 1–21.CrossRefGoogle Scholar
Sikorski, R. (1964), Boolean Algebras (Springer-Verlag, New York).Google Scholar
Taylor, A. E. (1958), Introduction to Functional Analysis (Wiley, New York).Google Scholar