科研之友
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摘要
We call a real number normal if for any block of digits the asymptotic frequency of this block in the N-adic expansion equals the expected one. In the present paper we consider non-normal numbers and, in particular, essentially and extremely non-normal numbers. We call a real number essentially non-normal if for each single digit there exists no asymptotic frequency of its occurrence. Furthermore we call a real number extremely non-normal if all possible probability vectors are accumulation points of the sequence of frequency vectors. Our aim now is to extend and generalize these results to Markov partitions.
- 出版日期2014-2
