Genericity and UD-random reals
نویسندگان
چکیده
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. 2000 Mathematics Subject Classification 03D32 (primary); 03D80 (secondary)
منابع مشابه
Uniform distribution and algorithmic randomness
Abstract. A seminal theorem due to Weyl [14] states that if (an) is any sequence of distinct integers, then, for almost every x ∈ R, the sequence (anx) is uniformly distributed modulo one. In particular, for almost every x in the unit interval, the sequence (anx) is uniformly distributed modulo one for every computable sequence (an) of distinct integers. Call such an x UD random. Here it is sho...
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تاریخ انتشار 2015