292 research outputs found
Genericity and UD-random reals
Avigad introduced the notion of UD–randomness based in Weyl’s 1916 definition of uniform distribution modulo one. We prove that there exists a weakly 1–random real that is neither UD–random nor weakly 1–generic. We also show that no 2–generic real can Turing compute a UD–random real
Lowness and Î nullsets
We prove that there exists a noncomputable c.e. real which is low for weak 2-randomness, a definition of randomness due to Kurtz, and that all reals which are low for weak 2-randomness are low for Martin-Lof randomness
Lowness notions, measure and domination
We show that positive measure domination implies uniform almost everywhere
domination and that this proof translates into a proof in the subsystem
WWKL (but not in RCA) 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 -randomness is the same as low for
Martin-L\"of randomness (a result independently obtained by Nies). Using the
same technique, we show that implies , generalizing the
fact that low for Martin-L\"of randomness implies low for
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