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A strong law of large numbers for random upper semicontinuous functions under exchangeability conditions

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  • Terán, Pedro

Abstract

In this paper we prove a strong law of large numbers for random upper semicontinuous functions on a separable Banach space possibly having unbounded support. Convergence is in a topology closely related to the Puri-Ralescu d[infinity] metric. Assumptions on the sequence of random variables are of exchangeability and uncorrelatedness type.

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  • Terán, Pedro, 2003. "A strong law of large numbers for random upper semicontinuous functions under exchangeability conditions," Statistics & Probability Letters, Elsevier, vol. 65(3), pages 251-258, November.
    • Handle: RePEc:eee:stapro:v:65:y:2003:i:3:p:251-258
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    1. López-Diaz, Miguel & Gil, Maria Angeles, 1997. "Constructive definitions of fuzzy random variables," Statistics & Probability Letters, Elsevier, vol. 36(2), pages 135-143, December.
    2. Colubi, Ana & Santos Domínguez-Menchero, J. & López-Díaz, Miguel & Körner, Ralf, 2001. "A method to derive strong laws of large numbers for random upper semicontinuous functions," Statistics & Probability Letters, Elsevier, vol. 53(3), pages 269-275, June.
    3. Hiai, Fumio & Umegaki, Hisaharu, 1977. "Integrals, conditional expectations, and martingales of multivalued functions," Journal of Multivariate Analysis, Elsevier, vol. 7(1), pages 149-182, March.
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    Cited by:

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