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, Online first, 11 p.

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:
Online First:
DOI: 10.5802/aif.3663
Classification: 42A55
Keywords: Good sequences, Uncountable spectrum.
Mot 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) 
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Cuny, Christophe; Parreau, François. Good sequences with uncountable spectrum and singular asymptotic distribution. Annales de l'Institut Fourier, Online first, 11 p.

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