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2013 | OriginalPaper | Buchkapitel

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

verfasst von : C. Castaing, P. Raynaud de Fitte

Erschienen in: Advances in Mathematical Economics Volume 17

Verlag: Springer Japan

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Abstract

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.

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Nächstes Kapitel Discounted optimal growth in a two-sector RSS model: a further geometric investigation
Fußnoten
1
Namely \(\sum _{k=1}^{n}1_{A_{k}}g_{k}\) is a convex combination with positive rational coefficients of functions in S X 1(ℱ X ).
 
2
For more details, one may consult the proof of Theorem 5.5 below.
 
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Metadaten
Titel
Law of large numbers and Ergodic Theorem for convex weak star compact valued Gelfand-integrable mappings
verfasst von
C. Castaing
P. Raynaud de Fitte
Copyright-Jahr
2013
Verlag
Springer Japan
Buch
Advances in Mathematical Economics Volume 17

Print ISBN: 978-4-431-54323-7

Electronic ISBN: 978-4-431-54324-4

Copyright-Jahr: 2013

DOI
https://doi.org/10.1007/978-4-431-54324-4_1