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

 

Infinite free set for small measure set mappings


Authors: Ludomir Newelski, Janusz Pawlikowski and Witold Seredyński
Journal: Proc. Amer. Math. Soc. 100 (1987), 335-339
MSC: Primary 04A05; Secondary 04A20, 28A25
MathSciNet review: 884475
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Abstract: A set $ A \subset X$ is free for a function $ F:X \to \mathcal{P}(X)$ provided $ x \notin F(y)$ for any distinct $ x,y \in A$. We show that, if $ F$ maps the reals into closed subsets of measure less than 1, then there is an infinite free set for $ F$. This solves Problem 38(B) of Erdös and Hajnal [EH].


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1987-0884475-3
PII: S 0002-9939(1987)0884475-3
Keywords: Set mapping, free set, Fubini's theorem
Article copyright: © Copyright 1987 American Mathematical Society