Abstract
AbstractA 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 measuretheoretic 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.
Publisher
Cambridge University Press (CUP)
Reference60 articles.
1. Recursively enumerable sets of positive integers and their decision problems
2. Nies André , Reals which compute little, In Chatzidakis et al. [6], pp. 260–274.
3. Zur Deutung der intuitionistischen Logik
4. Simpson Stephen G. , Mass problems and randomness, this Bulletin, vol. 11 (2005), pp. 1–27.
5. An extension of the recursively enumerable Turing degrees
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