Mass problems and measure-theoretic regularity
A well known fact is that every Lebesgue measurable set is regular, i.e., it includes an Fσ 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 ω-models of RCA0 which are relevant for the reverse mathematics of measure-theoretic regularity.
Permanent link to this document: http://projecteuclid.org/euclid.bsl/1255526079
Digital Object Identifier: doi:10.2178/bsl/1255526079
Zentralblatt MATH identifier: 05654340
Mathematical Reviews number (MathSciNet): MR2682785