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Proceedings of the American Mathematical Society

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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].

References [Enhancements On Off] (What's this?)

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Keywords: Set mapping, free set, Fubini's theorem
Article copyright: © Copyright 1987 American Mathematical Society