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Lebesgue Convergence Theorems and Reverse Mathematics

✍ Scribed by Xiaokang Yu

Publisher
John Wiley and Sons
Year
1994
Tongue
English
Weight
650 KB
Volume
40
Category
Article
ISSN
0044-3050

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✦ Synopsis

Abstract

Concepts of L^1^ 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 KΓΆnig'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 KΓΆnig's lemma.

Mathematics Subject Classification: 03F35.

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