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On conditional compactly uniform pth-order integrability of random elements in Banach spaces

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  • Cabrera, Manuel Ordóñez
  • Volodin, Andrei I.
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    Abstract

    The notion of conditional compactly uniform pth-order integrability of an array of random elements in a separable Banach space concerning an array of random variables and relative to a sequence of [sigma]-algebras is introduced and characterized. We state a conditional law for randomly weighted sums of random elements in a Banach space with the bounded approximation property, and we prove that, under the introduced condition, the problem can be reduced to a similar problem for random elements in a finite-dimensional space.

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    Bibliographic Info

    Article provided by Elsevier in its journal Statistics & Probability Letters.

    Volume (Year): 55 (2001)
    Issue (Month): 3 (December)
    Pages: 301-309

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    Handle: RePEc:eee:stapro:v:55:y:2001:i:3:p:301-309

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    Related research

    Keywords: Random elements Randomly weighted sums Conditional compactly uniform pth-order integrability Conditional tightness Conditional uniform integrability Bounded approximation property Schauder basis;

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