| Summary: | This paper establishes a mean convergence theorem for triangular
arrays of rowwise and pairwise mn-dependent random variables.
Some authors studied limit theorems for sequences of pairwise
m-dependent random variables where m is fixed (see, e.g., Quang
and Nguyen [Applications of Mathematics, 2016] and Thanh
[Bulletin of the Institute of Mathematics Academia Sinica,
2005]). In this paper, we establish a limit theorem for triangular
arrays of rowwise and pairwise mn-dependent random variables,
where mn may approach infinity as n → ∞. The main theorem
extends some results in the literature, including Theorem 3.1 of
Chen, Bai and Sung in [Journal of Mathematical Analysis and
Applications, 2014].
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