Law of large numbers and ergodic theorem for convex weak star compact valued Gelfand-integrable mappings

International audience; 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 largenumbers 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.