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Wilansky's query on outer measures

Published online by Cambridge University Press:  17 April 2009

Choo-Whan Kim
Choo-Whan Kim
Affiliation:
Department of Mathematics and Statistics, Simon Fraser University, Burnaby, British Columbia V5A 1S6, Canada.
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Abstract

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On a set X, let μ* be an outer measure and μ the measure induced by μ*. We show that if X is a finite set, then the measure μ is saturated. We give two examples of non-regular outer measures on an infinite set X which induce non-saturated and saturated measures, respectively. These answer a query posed by Wilansky.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 31 , Issue 3 , June 1985 , pp. 325 - 328
Copyright
Copyright © Australian Mathematical Society 1985

References

[1]Halmos, Paul R., Measure theory (Van Nostrand, New York, 1954).Google Scholar
[2]Royden, H.L., Real analysis, 2nd ed. (Macmillan, New York, 1968).Google Scholar
[3]Wilansky, A., “Query 305”, Notices Amer. Math. Soc. 31 (1984), 376.Google Scholar