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S-uniform scalar integrability and strong laws of large numbers for Pettis integrable functions with values in a separable locally convex space
- Source :
- Journal of Theoretical Probability, Journal of Theoretical Probability, Springer, 2000, 13 (1), pp.93-134. ⟨10.1023/A:1007782825974⟩
- Publication Year :
- 2000
- Publisher :
- HAL CCSD, 2000.
-
Abstract
- International audience; Generalizing techniques developed by Cuesta and Matran 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 $E$.
- Subjects :
- Skorokhod representation
[MATH.MATH-PR]Mathematics [math]/Probability [math.PR]
Mathematics::Functional Analysis
Kantorovich functional
Wasserstein metric
pairwise independent
Pettis
Glivenko--Cantelli
Pettis uniformly integrable
Strong law of large numbers
[MATH.MATH-FA]Mathematics [math]/Functional Analysis [math.FA]
Young measure
Subjects
Details
- Language :
- English
- ISSN :
- 08949840 and 15729230
- Database :
- OpenAIRE
- Journal :
- Journal of Theoretical Probability, Journal of Theoretical Probability, Springer, 2000, 13 (1), pp.93-134. ⟨10.1023/A:1007782825974⟩
- Accession number :
- edsair.dedup.wf.001..c574d6615b111fa7cfd9c8f6fdc1831e