Date: October 23, 1996
Title: Vitali's theorem and WWKL
Authors: Douglas K. Brown, Mariagnese Giusto, Stephen G. Simpson
Author e-mail: simpson@math.psu.edu
Available: http://www.math.psu.edu/simpson/papers/vitali.ps
Format: PostScript file (AMS-LaTeX source is also available)
Abstract: This paper is a contribution to the program of
Reverse Mathematics. We investigate the role of strong set
existence axioms in measure theory. Earlier work of Yu and
Simpson (Archive for Mathematical Logic, vol. 30, 1990,
pp. 171-180) showed that weak weak K"onig's lemma (WWKL) is
equivalent to countable additivity of Lebesgue measure on
open sets. We now show that WWKL is equivalent to the
Vitali covering theorem.
Publication: accepted April 17, 1998 for publication in
Archive for Mathematical Logic.