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Proceedings of the American Mathematical Society

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A solution of Ulam's problem on relative measure

Author: Tim Carlson
Journal: Proc. Amer. Math. Soc. 94 (1985), 129-134
MSC: Primary 03E25; Secondary 03E75, 28A05
MathSciNet review: 781070
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Abstract: Suppose $ \mathcal{A}$ is a collection of subsets of the unit interval and, for $ A \in \mathcal{A}$, $ {\mu _A}$ is a Borel measure on $ A$ which vanishes on points and gives $ A$ measure 1. The system $ {\mu _A}(A \in \mathcal{A})$ is called a coherent system if $ {\mu _A}(C) = {\mu _A}(B){\mu _B}(C)$ whenever $ A$ $ B \supseteq C$ are in $ \mathcal{A}$ and all terms are defined. The existence of a coherent system for the collection of perfect sets is shown to be independent of Zermelo-Fraenkel set theory with the axiom of dependent choices.

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

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Keywords: Coherent system, forcing, perfect tree, universal measure zero
Article copyright: © Copyright 1985 American Mathematical Society

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