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arXiv · 1408.2898

Lowness notions, measure and domination

Bjørn Kjos-Hanssen·Joseph S. Miller·Reed Solomon
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Abstract

We show that positive measure domination implies uniform almost everywhere domination and that this proof translates into a proof in the subsystem WWKL$_0$ (but not in RCA$_0$) of the equivalence of various Lebesgue measure regularity statements introduced by Dobrinen and Simpson. This work also allows us to prove that low for weak $2$-randomness is the same as low for Martin-Löf randomness (a result independently obtained by Nies). Using the same technique, we show that $\leq_{LR}$ implies $\leq_{LK}$, generalizing the fact that low for Martin-Löf randomness implies low for $K$.

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BibTeXRIS

Bjørn Kjos-Hanssen, Joseph S. Miller, Reed Solomon. 2014-08-13. Lowness notions, measure and domination. https://doi.org/10.1112/jlms%2Fjdr072

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