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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Nonmetric compact spaces and nonmeasurable processes


Author: R. M. Dudley
Journal: Proc. Amer. Math. Soc. 108 (1990), 1001-1005
MSC: Primary 60G05; Secondary 28A20, 60B05
MathSciNet review: 994775
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Abstract: Measure theory in compact Hausdorff spaces has some pathological aspects. Some natural functions are nonmeasurable. Others are measurable but have nonmeasurable ranges. Joint measurability is not preserved by the Kakutani-Nelson canonical representation of functions as elements of product spaces, even "almost", for the indicator function of the triangle below the diagonal of the unit square (empirical distribution function for sample size $ n = 1$).


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1990-0994775-4
PII: S 0002-9939(1990)0994775-4
Keywords: Kakutani-Nelson construction, joint measurability
Article copyright: © Copyright 1990 American Mathematical Society