David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
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Journal of Symbolic Logic 71 (3):1057 - 1072 (2006)
We explore the interaction between Lebesgue measure and dominating functions. We show, via both a priority construction and a forcing construction, that there is a function of incomplete degree that dominates almost all degrees. This answers a question of Dobrinen and Simpson, who showed that such functions are related to the proof-theoretic strength of the regularity of Lebesgue measure for Gδ sets. Our constructions essentially settle the reverse mathematical classification of this principle
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George Barmpalias (2012). Tracing and Domination in the Turing Degrees. Annals of Pure and Applied Logic 163 (5):500-505.
Jeremy Avigad, Edward T. Dean & Jason Rute (2012). Algorithmic Randomness, Reverse Mathematics, and the Dominated Convergence Theorem. Annals of Pure and Applied Logic 163 (12):1854-1864.
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