Construction of μ-normal sequences

Construction of μ-normal sequences

In the present paper we extend Champernowne’s construction of normal numbers to provide sequences which are generic for a given invariant probability measure, which need not be the maximal one. We present a construction together with estimates and examples for normal numbers with respect to Lüroth s...

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Veröffentlicht in:Monatshefte für Mathematik 2016-02, Vol.179 (2), p.259-280
Hauptverfasser: Madritsch, Manfred G., Mance, Bill
Format: Artikel
Sprache:eng
Schlagworte:
Mathematics
Mathematics and Statistics
Number Theory
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Zusammenfassung:In the present paper we extend Champernowne’s construction of normal numbers to provide sequences which are generic for a given invariant probability measure, which need not be the maximal one. We present a construction together with estimates and examples for normal numbers with respect to Lüroth series expansion, continued fractions expansion or β -expansion.
ISSN:0026-9255
1436-5081
DOI:10.1007/s00605-015-0837-1