Journal of Theoretical Probability

, Volume 13, Issue 1, pp 93–134 | Cite as

\(\mathfrak{S}\)-Uniform Scalar Integrability and Strong Laws of Large Numbers for Pettis Integrable Functions with Values in a Separable Locally Convex Space

  • Charles Castaing
  • Paul Raynaud de Fitte


Generalizing techniques developed by Cuesta and Matrán for Bochner integrable random vectors of a separable Banach space, we prove a strong law of large numbers for Pettis integrable random elements of a separable locally convex space E. This result may be seen as a compactness result in a suitable topology on the set of Pettis integrable probabilities on E.

strong law of large numbers pairwise independent Pettis Skorokhod's representation \(\mathfrak{S}\)-uniformly scalarly integrable Kantorovich functional Lévy–Wasserstein metric Young measures 


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© Plenum Publishing Corporation 2000

Authors and Affiliations

  • Charles Castaing
  • Paul Raynaud de Fitte

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