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Vitali's Theorem and WWKL

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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.

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Authors and Affiliations

  1. 145 CLRC, Penn State Altoona, Altoona, PA 16601, USA. e-mail: dkb5@psu.edu, , , , , , US

    Douglas K. Brown

  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

    Mariagnese Giusto

  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

    Stephen G. Simpson

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  1. Douglas K. Brown
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  2. Mariagnese Giusto
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  3. Stephen G. Simpson
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Received: 3 April 1998 / Published online: 3 October 2001

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Brown, D., Giusto, M. & Simpson, S. Vitali's Theorem and WWKL. Arch. Math. Logic 41, 191–206 (2002). https://doi.org/10.1007/s001530100100

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  • DOI: https://doi.org/10.1007/s001530100100

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