Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 03E25, 03E75, 28A05

Retrieve articles in all journals with MSC: 03E25, 03E75, 28A05


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1985-0781070-X
PII: S 0002-9939(1985)0781070-X
Keywords: Coherent system, forcing, perfect tree, universal measure zero
Article copyright: © Copyright 1985 American Mathematical Society