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A complete convergence theorem for row sums from arrays of rowwise independent random elements in Rademacher type $$p$$ Banach spaces. (English) Zbl 1237.60022
Summary: We extend in several directions a complete convergence theorem for row sums from an array of row-wise independent random variables obtained by S. H. Sung, A. I. Volodin and T.-C. Hu [Stat. Probab. Lett. 71, No. 4, 303–311 (2005; Zbl 1087.60030)] to an array of row-wise independent random elements taking values in a real separable Rademacher type $$p$$ Banach space. An example is presented which illustrates that our result extends the result in [loc. cit.] even for the random variable case.

##### MSC:
 60F15 Strong limit theorems 60B12 Limit theorems for vector-valued random variables (infinite-dimensional case) 60B11 Probability theory on linear topological spaces
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##### References:
 [1] DOI: 10.1073/pnas.33.2.25 · Zbl 0030.20101 · doi:10.1073/pnas.33.2.25 [2] DOI: 10.1214/aoms/1177730037 · Zbl 0033.29001 · doi:10.1214/aoms/1177730037 [3] DOI: 10.1080/07362999908809645 · Zbl 0940.60032 · doi:10.1080/07362999908809645 [4] Taylor , R.L. ( 1978 ).Stochastic Convergence of Weighted Sums of Random Elements in Linear Spaces.Lecture Notes in Mathematics, Vol. 672. Springer-Verlag, Berlin. · Zbl 0443.60004
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