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Unions of products of independent sets

Part of: Classical measure theory

Published online by Cambridge University Press:  26 February 2010

Zoltán Buczolich
Zoltán Buczolich
Affiliation:
Department of Analysis, Eötvös Loránd University, Múzeum krt. 6-8, Budapest, Hungary, H-1088.
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Abstract

We show that there exists an open set H⊆[0, 1] × [0, 1] with λ2(H) = 1 such that for any ε > 0 there exists a set E satisfying and H contains the product set E × E but there is no set S with and S × S ⊆ H. Especially this property is verified for sets of the form H = where the sets Ei are independent and . The results of this paper answer questions of M. Laczkovich and are related to a paper of D. H. Fremlin.

MSC classification

Secondary: 28A35: Measures and integrals in product spaces
Type
Research Article
Information
Mathematika , Volume 42 , Issue 1 , June 1995 , pp. 25 - 29
Copyright
Copyright © University College London 1995

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References

1.Freralin, D. H.. Covering squares with independent squares. Mathematika, 38 (1991), 329–333.Google Scholar
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