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A note on generalized unique extension of measures*

Published online by Cambridge University Press:  09 April 2009

Deng-Yuan Huang
Deng-Yuan Huang
Affiliation:
Institute of MathematicsAcademia Sinica Republic of, China
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In Theorem 1, we shall discuss some properties of semifinite measure, that is, the measure μ on a ring R of sets with the property that, for every E in R, μ(E) is equal to the least upper bound of μ(F) where F runs over sets such that F is in R (F ⊂ E) and μ(F) < ∞. Let σ(R) be the σ-ring generated by R. To prove Theorem 2 we shall use the uniqueness theorem in Luther's paper [2], which is stated as a lemma in this paper.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 14 , Issue 1 , July 1972 , pp. 59 - 61
Copyright
Copyright © Australian Mathematical Society 1972

References

[1]Berberian, S. K., Measure and Integration, Macmillan (New York, 1965).Google Scholar
[2]Luther, N. Y., ‘Unique Extension and Product Measures’, Canad. J. Math. 19 (1967), 757–763.CrossRefGoogle Scholar