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On strong laws of large numbers for arrays of rowwise independent random elements. (English) Zbl 0844.60005
Summary: Let $$\{X_{nk}\}$$ be an array of rowwise independent random elements in a separable Banach space of type $$r$$, $$1 \leq r \leq 2$$. Complete convergence of $$n^{1/p} \sum^n_{k = 1} X_{nk}$$ to 0, $$0 < p < r \leq 2$$, is obtained when $$\sup_{1 \leq k \leq n} E|X_{nk}|^\nu = O(n^\alpha)$$, $$\alpha \geq 0$$, with $$\nu(1/p - 1/r) > \alpha + 1$$. An application to density estimation is also given.

##### MSC:
 60B12 Limit theorems for vector-valued random variables (infinite-dimensional case) 62G05 Nonparametric estimation 60F15 Strong limit theorems
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