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

Charles Castaing () and Paul Raynaud de Fitte ()

Journal of Theoretical Probability, 2000, vol. 13, issue 1, 93-134

Abstract: Abstract 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.

Keywords: strong law of large numbers; pairwise independent; Pettis; Skorokhod's representation; $$\mathfrak{S}$$ -uniformly scalarly integrable; Kantorovich functional; Lévy–Wasserstein metric; Young measures (search for similar items in EconPapers)
Date: 2000
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DOI: 10.1023/A:1007782825974

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