Mass Problems and Measure-Theoretic Regularity
| Autor: | Stephen G. Simpson |
|---|---|
| Rok vydání: | 2009 |
| Předmět: |
68Q30
Logic Lebesgue integration Lebesgue–Stieltjes integration Measure (mathematics) Muchnik degrees symbols.namesake Borel equivalence relation Borel hierarchy hyperarithmetical hierarchy Borel sets reverse mathematics LR-reducibility 03D80 Borel measure Mathematics Discrete mathematics Turing degrees Mathematics::Logic measure theory Philosophy 03D55 symbols Borel set 03D30 Descriptive set theory |
| Zdroj: | Bull. Symbolic Logic 15, iss. 4 (2009), 385-409 |
| ISSN: | 1943-5894 1079-8986 |
| DOI: | 10.2178/bsl/1255526079 |
| Popis: | 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 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. |
| Databáze: | OpenAIRE |
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