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Almost everywhere domination
 Journal of Symbolic Logic
"... Abstract. A Turing degree a is said to be almost everywhere dominating if, for almost all X 2 2ù with respect to the Òfair coinÓ probability measure on 2ù, and for all g: ù! ù Turing reducible to X, there exists f: ù! ù of Turing degree a which dominates g. We study the problem of characterizing the ..."
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Abstract. A Turing degree a is said to be almost everywhere dominating if, for almost all X 2 2ù with respect to the Òfair coinÓ probability measure on 2ù, and for all g: ù! ù Turing reducible to X, there exists f: ù! ù of Turing degree a which dominates g. We study the problem of characterizing the almost everywhere dominating Turing degrees and other, similarly deÞned classes of Turing degrees. We relate this problem to some questions in the reverse mathematics of measure theory. x1. Introduction. In this paper ù denotes the set of natural numbers, 2ù denotes the set of total functions from ù to f0; 1g, and ùù denotes the set of total functions from ù to ù. The Òfair coinÓ probability measure ì on 2ù is given by
The Baire category theorem in weak subsystems of secondorder arithmetic
 THE JOURNAL OF SYMBOLIC LOGIC
, 1993
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Mass problems and measuretheoretic regularity
, 2009
"... Research supported by NSF grants DMS0600823 and DMS0652637. ..."
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Cited by 6 (3 self)
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Research supported by NSF grants DMS0600823 and DMS0652637.
Vitali’s theorem and WWKL
 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 RCA0. We show that several wellknown measuretheoretic propositions ..."
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Cited by 3 (0 self)
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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 wellknown measuretheoretic propositions including the Vitali Covering Theorem are equivalent to WWKL over RCA0. 1.
Recommended Citation Rute, Jason, "Topics in algorithmic randomness and computable analysis " (2013). Dissertations. Paper 260.
, 2013
"... Topics in algorithmic randomness and computable analysis ..."
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