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Some results on strong limit theorems for (LB)-space-valued random variables

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  • Wang, Xaingchen
  • Bhaskara Rao, M.
  • Li, Deli

Abstract

Let E be a strict (LB)-space, i.e., a strict inductive limit of separable Banach spaces E1 [subset of] E2 [subset of] ... One of the results proved in this is the following. Let Xn, n [greater-or-equal, slanted] 1 be a sequence of independent identically distributed (i.i.d.) random variables taking values in E. If the Strong law of large numbers holds for this sequence, i.e., (1/m)[summation operator]i = 1m Xi, m [greater-or-equal, slanted] 1 converges almost surely, then there exists n [greater-or-equal, slanted] 1 such that each Xi takes values in En almost surely.

Suggested Citation

  • Wang, Xaingchen & Bhaskara Rao, M. & Li, Deli, 1995. "Some results on strong limit theorems for (LB)-space-valued random variables," Statistics & Probability Letters, Elsevier, vol. 23(3), pages 247-251, May.
    • Handle: RePEc:eee:stapro:v:23:y:1995:i:3:p:247-251
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    References listed on IDEAS

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    1. Suchanek, Ana Mari­a, 1978. "On almost sure convergence of Cesaro averages of subsequences of vector-valued functions," Journal of Multivariate Analysis, Elsevier, vol. 8(4), pages 589-597, December.
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