A solution of Ulam’s problem on relative measure
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- by Tim Carlson PDF
- Proc. Amer. Math. Soc. 94 (1985), 129-134 Request permission
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
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Additional Information
- © Copyright 1985 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 94 (1985), 129-134
- MSC: Primary 03E25; Secondary 03E75, 28A05
- DOI: https://doi.org/10.1090/S0002-9939-1985-0781070-X
- MathSciNet review: 781070