Vitali's Theorem and WWKL

Douglas K. Brown
Mariagnese Giusto
Stephen G. Simpson

simpson@math.psu.edu
Pennsylvania State University
October 25, 1998

Giusto's research was partially supported by Funds 40% of MURST of Italy. Simpson's research was partially supported by NSF grant DMS-9303478.

Accepted April 17, 1998 for Archive for Mathematical Logic.

Abstract:

Continuing the investigations of X. Yu and others, we study the role of set existence axioms in classical Lebesgue measure theory. We show that pairwise disjoint countable additivity for open sets of reals is provable in $\mathsf{RCA}_0$. We show that several well-known measure-theoretic propositions including the Vitali Covering Theorem are equivalent to WWKL over $\mathsf{RCA}_0$.