Abstract <p>This paper aims to establish some limit theorems for the multidimensional arrays of random variables under capacities, such as Fatou’s lemma, Lebesgue’s dominated convergence theorem, and especially, the strong law of large numbers. To do this, we introduce the notion of the partial limit for array of real numbers and study the properties of the inferior limit and the superior limit of the array of real numbers. Our results extend some related results in the literature.</p>