A Turing degree a is said to be almost everywhere dominating if, for almost all X∈ 2ω with respect to the “fair coin” probability measure on 2ω, and for all g : ω→ω Turing reducible to X, there exists f : ω→ω of Turing degree a which dominates g. We study the problem of characterizing the almost everywhere dominating Turing degrees and other, similarly defined classes of Turing degrees. We relate this problem to some questions in the reverse mathematics of measure theory.
"Almost everywhere domination." J. Symbolic Logic 69 (3) 914 - 922, September 2004. https://doi.org/10.2178/jsl/1096901775