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Continuous and random Vapnik-Chervonenkis classes

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Abstract

Nous démontrons que si T est une théorie dépendante, sa randomisée de keisler T R l’est aussi.

Pour faire cela nous généralisons la notion d’une classe de Vapnik-Chervonenkis à des familles de fonctions à valeurs dans [0, 1] (dyune classe de Vapnik-Chervonenkis continue), et nous caractérisons les familles de fonctions ayant cette propriété par la vitesse de croissance de la largeur moyenne d’une famille de compacts convexes associés.

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Authors and Affiliations

  1. Université Lyon 1 INSA de Lyon, F-69621, École Centrale de Lyon CNRS UMR 5208, Institut Camille Jordan, Université de Lyon, 43 bd du 11 novembre 1918, F-69622, Villeurbanne-Cedex, France

    Itaï Ben Yaacov

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  1. Itaï Ben Yaacov
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Additional information

Research initiated during the workshop “Model theory of metric structures”, American Institute of Mathematics Research Conference Centre, 18 to 22 September 2006.

Research supported by ANR chaire d’excellence junior (projet THEMODMET) and by the European Commission Marie Curie Research Network ModNet.

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Ben Yaacov, I. Continuous and random Vapnik-Chervonenkis classes. Isr. J. Math. 173, 309–333 (2009). https://doi.org/10.1007/s11856-009-0094-x

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  • DOI: https://doi.org/10.1007/s11856-009-0094-x

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