Law of large numbers and Ergodic Theorem for convex weak star compact valued Gelfand-integrable mappings

  • C. CastaingEmail author
  • P. Raynaud de Fitte
Part of the Advances in Mathematical Economics book series (MATHECON, volume 17)


We prove several results in the integration of convex weak star (resp. norm compact) valued random sets with application to weak star Kuratowski convergence in the law of large numbers for convex norm compact valued Gelfand-integrable mappings in the dual of a separable Banach space. We also establish several weak star Kuratowski convergence in the law of large numbers and ergodic theorem involving the subdifferential operators of Lipschitzean functions defined on a separable Banach space, and also provide an application to a closure type result arisen in evolution inclusions.

Key words

Conditional expectation Ergodic Generalized directional derivative Law of large numbers Locally Lipschitzean Subdifferential 


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Copyright information

© Springer Japan 2013

Authors and Affiliations

  1. 1.Département de MathématiquesUniversité Montpellier IIMontpellier Cedex 5France
  2. 2.Laboratoire Raphaël Salem, UMR CNRS 6085, UFR SciencesUniversité de RouenSaint Etienne du RouvrayFrance

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