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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On some random thin sets of integers


Authors: Daniel Li, Hervé Queffélec and Luis Rodríguez-Piazza
Journal: Proc. Amer. Math. Soc. 136 (2008), 141-150
MSC (2000): Primary 43A46; Secondary 42A55, 42A61
Published electronically: October 12, 2007
MathSciNet review: 2350399
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Abstract: We show how different random thin sets of integers may have different behaviour. First, using a recent deviation inequality of Boucheron, Lugosi and Massart, we give a simpler proof of one of our results in Some new thin sets of integers in harmonic analysis, Journal d'Analyse Mathématique 86 (2002), 105-138, namely that there exist $ \frac{4}{3}$-Rider sets which are sets of uniform convergence and $ \Lambda (q)$-sets for all $ q < \infty $ but which are not Rosenthal sets. In a second part, we show, using an older result of Kashin and Tzafriri, that, for $ p > \frac{4}{3}$, the $ p$-Rider sets which we had constructed in that paper are almost surely not of uniform convergence.


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Additional Information

Daniel Li
Affiliation: Université d’Artois, Laboratoire de Mathématiques de Lens EA 2462–FR 2956, Faculté des Sciences Jean Perrin, 23, rue J. Souvraz SP 18, F-62307 Lens Cedex, France
Email: daniel.li@euler.univ-artois.fr

Hervé Queffélec
Affiliation: Laboratoire Paul Painlevé UMR CNRS 8524, U.F.R. de Mathématiques Pures et Appliquées, Bât. M2, Université des Sciences et Technologies de Lille 1, F-59665 Villeneuve d’Ascq Cedex, France
Email: Herve.Queffelec@math.univ-lille1.fr

Luis Rodríguez-Piazza
Affiliation: Universidad de Sevilla, Facultad de Matemáticas, Departamento de Análisis Matemático, Apartado de Correos 1160, 41080 Sevilla, Spain
Email: piazza@us.es

DOI: http://dx.doi.org/10.1090/S0002-9939-07-09049-1
PII: S 0002-9939(07)09049-1
Keywords: Boucheron-Lugosi-Massart deviation inequality, $\Lambda (q)$-sets, $p$-Rider sets, Rosenthal sets, selectors, sets of uniform convergence
Received by editor(s): September 19, 2006
Published electronically: October 12, 2007
Communicated by: Michael Lacey
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.