Mathematical Logic Quarterly 40 (1):1-13 (1994)

Abstract
Concepts of L1 space, integrable functions and integrals are formalized in weak subsystems of second order arithmetic. They are discussed especially in relation with the combinatorial principle WWKL (weak-weak König's lemma and arithmetical comprehension. Lebesgue dominated convergence theorem is proved to be equivalent to arithmetical comprehension. A weak version of Lebesgue monotone convergence theorem is proved to be equivalent to weak-weak König's lemma
Keywords Subsystems of second‐order arithmetic  Arithmetical comprehension  Lebesgue convergence theorems  Recursive comprehension  Measure theory  Weak Königs lemma  Reverse mathematics
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DOI 10.1002/malq.19940400102
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Vitali's Theorem and WWKL.Douglas K. Brown, Mariagnese Giusto & Stephen G. Simpson - 2002 - Archive for Mathematical Logic 41 (2):191-206.
A Nonstandard Counterpart of WWKL.Stephen G. Simpson & Keita Yokoyama - 2011 - Notre Dame Journal of Formal Logic 52 (3):229-243.
Almost Everywhere Domination.Natasha L. Dobrinen & Stephen G. Simpson - 2004 - Journal of Symbolic Logic 69 (3):914-922.
Mass Problems and Measure-Theoretic Regularity.Stephen G. Simpson - 2009 - Bulletin of Symbolic Logic 15 (4):385-409.

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