Vitali's theorem and WWKL
type: Item
instance of: scholarly article
title: Vitali's theorem and WWKL
zbMATH Open document ID: 1030.03044
author: Douglas K. Brown
author: Mariagnese Giusto
author: Stephen G. Simpson
published in: Archive for Mathematical Logic
publication date: 2003-09-16T00:00:00Z
review text: The authors analyze theorems of classical Lebesgue measure theory using the framework of reverse mathematics. Principal results include the provability of pairwise disjoint countable additivity for open sets in RCA\(_0\), and the equivalence of the system WWKL\(_0\) and the Vitali Covering Theorem. An interesting alternative intensional formulation of Lebesgue measure is introduced, accompanied by a proof in WWKL\(_0\) of the equivalence of this formulation with the previously used definition. The article concludes with a substantial bibliography which lists half a dozen related papers by \textit{X. Yu}, for example [Ann. Pure Appl. Logic 79, 211-219 (1996; Zbl 0855.03036)].
Mathematics Subject Classification ID: 03F35
Mathematics Subject Classification ID: 03F60
Mathematics Subject Classification ID: 03B30
Mathematics Subject Classification ID: 28E15
zbMATH DE Number: 1982469
zbMATH Keywords: Reverse mathematics
zbMATH Keywords: second-order arithmetic
zbMATH Keywords: constructive analysis
zbMATH Keywords: computable analysis
zbMATH Keywords: WWKL
zbMATH Keywords: Lebesgue measure theory
reviewed by: Jeffry L. Hirst
MaRDI profile type: Publication
full work available at URL: s001530100100
OpenAlex ID: W2037923170
DOI: 10.1007/S001530100100
description: scientific article; zbMATH DE number 1982469