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December 2009 Mass problems and measure-theoretic regularity
Stephen G. Simpson
Bull. Symbolic Logic 15(4): 385-409 (December 2009). DOI: 10.2178/bsl/1255526079

Abstract

A well known fact is that every Lebesgue measurable set is regular, i.e., it includes an F$_{\sigma}$ set of the same measure. We analyze this fact from a metamathematical or foundational standpoint. We study a family of Muchnik degrees corresponding to measure-theoretic regularity at all levels of the effective Borel hierarchy. We prove some new results concerning Nies's notion of LR-reducibility. We build some $\omega$-models of RCA$_0$which are relevant for the reverse mathematics of measure-theoretic regularity.

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Stephen G. Simpson. "Mass problems and measure-theoretic regularity." Bull. Symbolic Logic 15 (4) 385 - 409, December 2009. https://doi.org/10.2178/bsl/1255526079

Information

Published: December 2009
First available in Project Euclid: 14 October 2009

zbMATH: 1191.03007
MathSciNet: MR2682785
Digital Object Identifier: 10.2178/bsl/1255526079

Subjects:
Primary: 03D30, 03D55, 03D80, 68Q30

Rights: Copyright © 2009 Association for Symbolic Logic

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Vol.15 • No. 4 • December 2009
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