# Construction of μ -normal sequences

Abstract : 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 $\beta$-expansion.
Document type :
Journal articles

https://hal.archives-ouvertes.fr/hal-01316249
Submitted on : Monday, May 16, 2016 - 10:57:38 AM
Last modification on : Tuesday, October 9, 2018 - 4:12:49 PM

### Citation

Manfred G. Madritsch, Bill Mance. Construction of μ -normal sequences. Monatshefte für Mathematik, Springer Verlag, 2016, 179 (2), pp.259-280. ⟨10.1007/s00605-015-0837-1⟩. ⟨hal-01316249⟩

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