Brown, Douglas K.; Giusto, Mariagnese; Simpson, Stephen G. Vitali’s theorem and WWKL. (English) Zbl 1030.03044 Arch. Math. Logic 41, No. 2, 191-206 (2002). 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 X. Yu, for example [Ann. Pure Appl. Logic 79, 211-219 (1996; Zbl 0855.03036)]. Reviewer: Jeffry L.Hirst (Boone) Cited in 3 ReviewsCited in 11 Documents MSC: 03F35 Second- and higher-order arithmetic and fragments 03F60 Constructive and recursive analysis 03B30 Foundations of classical theories (including reverse mathematics) 28E15 Other connections with logic and set theory Keywords:Reverse mathematics; second-order arithmetic; constructive analysis; computable analysis; WWKL; Lebesgue measure theory Citations:Zbl 0855.03036 PDFBibTeX XMLCite \textit{D. K. Brown} et al., Arch. Math. Logic 41, No. 2, 191--206 (2002; Zbl 1030.03044) Full Text: DOI