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Products of Radon Measures: A Counter-Example

Published online by Cambridge University Press:  20 November 2018

D. H. Fremlin
D. H. Fremlin*
Affiliation:
University of Essex, Colchester, England
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Abstract

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I show that if X is the hyperstonian space of Lebesgue measure on [0,1], then there are open sets in X×X which are not measurable for the simple product outer measure. This answers a question of M. C. Godfrey and M. Sion.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 19 , Issue 3 , 01 September 1976 , pp. 285 - 289
Copyright
Copyright © Canadian Mathematical Society 1976

References

1. Berberian, S. K., Measure and Integration, Addison-Wesley 1971.Google Scholar
2. Bourbaki, N., Éléments de mathématique VI—Intégration, chaps. I-IV. Hermann, 1952 (A.S.I. 1175).Google Scholar
3. Dixmier, J., Sur certains espaces considérées par M. H. Stone, Summa Brasil. Math. 2 (1951) 151–182.Google Scholar
4. Erdös, P. and Oxtoby, J. C., Partitions of the plane into sets having positive measure in every non-null measurable product set, Trans. Amer. Math. Soc. 79 (1955) 91–102.Google Scholar
5. Fremlin, D. H., Topological Riesz Spaces and Measure Theory, Cambridge Univ. Press, 1974.Google Scholar
6. Godfrey, M. C. and M. Sion, On product of Radón measures, Canad. Math. Bull. 12 (1968) 427–444.Google Scholar
7. Halmos, P. R., Measure Theory, Van Nostrand, 1950.Google Scholar
8. Munroe, M. E., Measure and Integration, Addison-Wesley, 1971.Google Scholar