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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?)

  • [E] P. Erdös, Some remarks on set theory. III, Michigan Math. J. 2 (1953-54), 51-57. MR 0062806 (16:20e)
  • [EH] P. Erdös and A. Hajnal, Unsolved problems in set theory, Axiomatic Set Theory, Proc. Sympos. Pure Math., Vol. 13, Part 1, Amer. Math. Soc., Providence, R.I., 1971, pp. 17-48. MR 0280381 (43:6101)
  • [G] S. Gładysz, Bemerkungen über die Unabhangigkeit der Punkte in Bezug auf Mengenwertigen Funktionen, Acta Math. Acad. Sci. Hungar. 13 (1962), 199-201. MR 0173740 (30:3950)
  • [ŁM] J. Łoś and E. Marczewski, Extensions of measure, Fund. Math. 36 (1949), 267-276. MR 0035327 (11:717h)

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

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