Abstract#R##N##R##N#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 Konig'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 Konig's lemma.#R##N##R##N##R##N##R##N#Mathematics Subject Classification: 03F35.
['Xiaokang Yu']
Lebesgue Convergence Theorems and Reverse Mathematics