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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
Mass problems and measuretheoretic regularity
, 2009
"... Research supported by NSF grants DMS0600823 and DMS0652637. ..."
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Research supported by NSF grants DMS0600823 and DMS0652637.