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  1. Vitali's Theorem and WWKL.Douglas K. Brown, Mariagnese Giusto & Stephen G. Simpson - 2002 - Archive for Mathematical Logic 41 (2):191-206.
    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.
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  • Measure theory and weak König's lemma.Xiaokang Yu & Stephen G. Simpson - 1990 - Archive for Mathematical Logic 30 (3):171-180.
    We develop measure theory in the context of subsystems of second order arithmetic with restricted induction. We introduce a combinatorial principleWWKL (weak-weak König's lemma) and prove that it is strictly weaker thanWKL (weak König's lemma). We show thatWWKL is equivalent to a formal version of the statement that Lebesgue measure is countably additive on open sets. We also show thatWWKL is equivalent to a formal version of the statement that any Borel measure on a compact metric space is countably additive (...)
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