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A study of singular points and supports of measures in reverse mathematics
Annals of Pure and Applied Logic 79 (2):211-219 (1996)
Abstract
Arithmetical comprehension is proved to be equivalent to the enumerability of singular points of any measure on the Cantor space. It is provable in ACA0 that any perfect closed subset of [0, 1] is the support of some continuous positive linear functional on C[0, 1]Other Versions
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Citations of this work
Vitali's Theorem and WWKL.Douglas K. Brown, Mariagnese Giusto & Stephen G. Simpson - 2002 - Archive for Mathematical Logic 41 (2):191-206.
Almost everywhere domination.Natasha L. Dobrinen & Stephen G. Simpson - 2004 - Journal of Symbolic Logic 69 (3):914-922.
Mass problems and measure-theoretic regularity.Stephen G. Simpson - 2009 - Bulletin of Symbolic Logic 15 (4):385-409.
References found in this work
Which set existence axioms are needed to prove the separable Hahn-Banach theorem?Douglas K. Brown & Stephen G. Simpson - 1986 - Annals of Pure and Applied Logic 31:123-144.
Measure theory and weak König's lemma.Xiaokang Yu & Stephen G. Simpson - 1990 - Archive for Mathematical Logic 30 (3):171-180.
Riesz representation theorem, Borel measures and subsystems of second-order arithmetic.Xiaokang Yu - 1993 - Annals of Pure and Applied Logic 59 (1):65-78.
Friedman's Research on Subsystems of Second Order Arithmetic.Stephen G. Simpson - 1990 - Journal of Symbolic Logic 55 (2):870-874.
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