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Vitali's Theorem and WWKL |
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| Authors: | Douglas K Brown Mariagnese Giusto Stephen G Simpson |
| Institution: | (1) 145 CLRC, Penn State Altoona, Altoona, PA 16601, USA. e-mail: dkb5@psu.edu, US;(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) 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 |
| 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. Received: 3 April 1998 / Published online: 3 October 2001 |
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