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 show that 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.

• Type: Journal
• Year: 2002
• Where: AML
• Authors: Douglas K. Brown, Mariagnese Giusto, Stephen G. Simpson
• Keywords: AML 2002, Classical Lebesgue Measure, Existence Axioms, Well-known Measure-theoretic Propositions