Uniform almost everywhere domination

2005/06/01 by Peter Cholak, Joseph Miller, Cholak, Peter +3
Mathematics · #03D28 #03D30 #03D60 #FOS: Mathematics #Logic (math.LO) #math.LO #msc:03D28 #msc:03D30 #msc:03D60

paper · pdf · doi:10.48550/arxiv.math/0506019

arxiv created 2005/11/14 · arxiv updated 2009/12/01

Abstract

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 G_δ sets. Our constructions essentially settle the reverse mathematical classification of this principle. Revised Nov 13, 2005. Minor corrections made.

Related

• A Lower Bound for Generalized Dominating Numbers
• Sharpness of Lenglart's domination inequality and a sharp monotone version
• Sparse domination and L^p → L^q estimates for maximal functions associated with curvature
• Comparing the closed almost disjointness and dominating numbers
• On uniform distribution for invariant extensions of the linear Lebesgue measure