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Property kα,n on Spaces with Strictly Positive Measure

Published online by Cambridge University Press:  20 November 2018

S. Argyros  and
N. Kalamidas
S. Argyros
Affiliation:
Athens University, Athens, Greece
N. Kalamidas
Affiliation:
Athens University, Athens, Greece
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In this paper we study intersection properties of measurable sets with positive measure in a probability measure space, or equivalently, intersection properties of open subsets on a compact space with a strictly positive measure.

The first result in this direction is due to Erdös and it is a negative solution to the problem of calibers on such spaces. In particular, under C.H., Erdös proved that Stone's space of Lebesque measurable sets of [0, 1] modulo null sets, does not have ℵ1-caliber.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 34 , Issue 5 , 01 October 1982 , pp. 1047 - 1058
Copyright
Copyright © Canadian Mathematical Society 1982

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