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On the strong law of large numbers and -convergence for double arrays of random elements in p-uniformly smooth Banach spaces

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  • Quang, Nguyen Van
  • Huan, Nguyen Van

Abstract

The aim of this paper is to establish some strong laws of large numbers and -convergence for double arrays of random elements in p-uniformly smooth Banach spaces. We also provide a new characterization of p-uniformly smooth Banach spaces in terms of a strong law of large numbers for double arrays.

Suggested Citation

  • Quang, Nguyen Van & Huan, Nguyen Van, 2009. "On the strong law of large numbers and -convergence for double arrays of random elements in p-uniformly smooth Banach spaces," Statistics & Probability Letters, Elsevier, vol. 79(18), pages 1891-1899, September.
    • Handle: RePEc:eee:stapro:v:79:y:2009:i:18:p:1891-1899
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    References listed on IDEAS

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    1. Adler, André & Rosalsky, Andrew & Volodin, Andrej I., 1997. "A mean convergence theorem and weak law for arrays of random elements in martingale type p Banach spaces," Statistics & Probability Letters, Elsevier, vol. 32(2), pages 167-174, March.
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    Cited by:

    1. Castaing, Charles & Quang, Nguyen Van & Thuan, Nguyen Tran, 2012. "A new family of convex weakly compact valued random variables in Banach space and applications to laws of large numbers," Statistics & Probability Letters, Elsevier, vol. 82(1), pages 84-95.
    2. Quang, Nguyen Van & Nguyen, Pham Tri, 2015. "Some strong laws of large number for double array of random upper semicontinuous functions in convex combination spaces," Statistics & Probability Letters, Elsevier, vol. 96(C), pages 85-94.
    3. Son, Ta Cong & Thang, Dang Hung & Dung, Le Van, 2012. "Rate of complete convergence for maximums of moving average sums of martingale difference fields in Banach spaces," Statistics & Probability Letters, Elsevier, vol. 82(11), pages 1978-1985.

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