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On measures on complete Boolean algebras

Published online by Cambridge University Press:  12 March 2014

Karel Prikry
Karel Prikry*
Affiliation:
University of Wisconsin, Madison, Wisconsin 53706
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Extract

In this paper we prove some theorems concerning measures on complete Boolean algebras. Among other things, in §I of this paper, we construct a counterexample to the following conjecture of W. Luxemburg: Every measure on a nonatomic hyperstonian Boolean algebra is normal. (See [3, p. 57].) This result is expressed by Theorem 1, §I. In order to construct this example we have to suppose that a real-valued measurable cardinal exists. This hypothesis is independent of the usual axioms of set theory. Luxemburg proved that our assumption is necessary. Our second result is stated in Theorem 2 near the end of the paper.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 36 , Issue 3 , September 1971 , pp. 395 - 406
Copyright
Copyright © Association for Symbolic Logic 1972

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References

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