MASS PROBLEMS AND MEASURE-THEORETIC REGULARITY

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.