Mean Convergence Theorem for Multidimensional Arrays of Random Elements in Banach Spaces
نویسنده
چکیده
where (n1,n2, . . . ,nd)= n∈ Z+. Recently, Thanh [11] proved (1.1) under condition of uniform integrability of {|Xn|p, n∈ Z+}. Mean convergence theorems for sums of random elements Banach-valued are studied by many authors. The reader may refer to Wei and Taylor [12], Adler et al. [2], Rosalsky and Sreehari [9], or more recently, Rosalsky et al. [10], Cabrera and Volodin [3]. However, we are unaware of any literature of investigation on the mean convergence for multidimensional arrays of random elements in Banach spaces. Consider a d-dimensional array {Vn, n ∈ Z+} of independent random elements defined on a probability space (Ω, ,P) and taking values in a real separable Banach space
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