no. 3
Good sequences with uncountable spectrum and singular asymptotic distribution
Cuny, Christophe1; Parreau, François2
1 Univ Brest, CNRS, UMR 6205, Laboratoire de Mathematiques de Bretagne Atlantique, 6 avenue Victor Le Gorgeu, 29238 Brest (France)
2 Université Sorbonne Paris Nord, LAGA, CNRS, UMR 7539, F-93430 Villetaneuse (France)
Annales de l'Institut Fourier, Volume 75 (2025) no. 3, pp. 967-977.

We construct a good sequence with uncountable spectrum. The construction also allows us to exhibit a continuous and singular probability measure representable by a good sequence in the sense of the recent work of Lesigne, Quas, Rosenblatt and Wierdl.

Nous construisons une bonne suite à spectre non dénombrable. La construction nous permet également d’exhiber une probabilité continue singulière représentable par une bonne suite au sens du travail récent de Lesigne, Quas, Rosenblatt et Wierdl.

Received:
Revised:
Accepted:
Published online:
DOI: 10.5802/aif.3663
Classification: 42A55
Keywords: Good sequences, Uncountable spectrum.
Mots-clés : Bonnes suites, spectre non dénombrable.

Cuny, Christophe 1; Parreau, François 2

1 Univ Brest, CNRS, UMR 6205, Laboratoire de Mathematiques de Bretagne Atlantique, 6 avenue Victor Le Gorgeu, 29238 Brest (France)
2 Université Sorbonne Paris Nord, LAGA, CNRS, UMR 7539, F-93430 Villetaneuse (France)
License: CC-BY-ND 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
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Cuny, Christophe; Parreau, François. Good sequences with uncountable spectrum and singular asymptotic distribution. Annales de l'Institut Fourier, Volume 75 (2025) no. 3, pp. 967-977. doi : 10.5802/aif.3663. https://aif.centre-mersenne.org/articles/10.5802/aif.3663/

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