Vitali's Theorem and WWKL

Vitali's Theorem and WWKL

Continuing the investigations of X. Yu and others, we study the role of set existence axioms in classical Lebesgue measure theory. We showthat pairwise disjoint countable additivity for open sets of reals is provable in RCA0. We show that several well-known measure-theoretic propositions including t...

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Veröffentlicht in:Archive for mathematical logic 2002-02, Vol.41 (2), p.191-206
Hauptverfasser: Brown, Douglas K., Giusto, Mariagnese, Simpson, Stephen G.
Format: Artikel
Sprache:eng
Schlagworte:
Logic
Mathematics
Theory
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Zusammenfassung:Continuing the investigations of X. Yu and others, we study the role of set existence axioms in classical Lebesgue measure theory. We showthat pairwise disjoint countable additivity for open sets of reals is provable in RCA0. We show that several well-known measure-theoretic propositions including the Vitali Covering Theorem are equivalent to WWKL over RCA0.
ISSN:0933-5846
1432-0665
DOI:10.1007/s001530100100