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Archive for Mathematical Logic

, Volume 41, Issue 2, pp 191–206 | Cite as

Vitali's Theorem and WWKL

  • Douglas K. Brown
  • Mariagnese Giusto
  • Stephen G. Simpson

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 RCA0. We show that several well-known measure-theoretic propositions including the Vitali Covering Theorem are equivalent to WWKL over RCA0.

Keywords

Lebesgue Measure Pairwise Disjoint Measure Theory Countable Additivity Covering Theorem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Douglas K. Brown
    • 1
  • Mariagnese Giusto
    • 2
  • Stephen G. Simpson
    • 3
  1. 1.145 CLRC, Penn State Altoona, Altoona, PA 16601, USA. e-mail: dkb5@psu.eduUS
  2. 2.Via Loreto Vecchia 9/10/A, 17100 Savona, Italy. e-mail: mariagnese@savonaonline.it Research partially supported by Funds 40% of MURST of Italy.IT
  3. 3.Department of Mathematics, Pennsylvania State University, 333 McAllister Building, University Park, State College, PA 16802, USA. e-mail: simpson@math.psu.edu Research partially supported by NSF grant DMS-9393478.US

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