Subsequences of normal sequences |
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Authors: | Teturo Kamae |
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Institution: | (1) Department of Mathematics, Osaka City University, Sugimoto-cho, Osaka, Japan |
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Abstract: | In this paper, we characterize a set of indices τ={τ(0)<τ(1)<…} such that forany normal sequence (α(0), α(1),…) of a certain type, the subsequence (α(τ(0)), α(τ(1)),…) is a normal sequence of the same type.
Assume thatn→∞. Then, we prove that τ has this property if and only if the 0–1 sequence (θ
τ
(0), whereθ
τ
(i)=1 or 0 according asi∈{τ(j);j=0, 1,…} or not, iscompletely deterministic in the sense of B. Weiss. |
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Keywords: | |
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