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.
Citation
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
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