The aim of this paper is to establish some strong laws of large numbers for double array of random upper semicontinuous functions in convex combination space under various assumptions. Our results generalize some related previously reported results.

In this paper, we suggest a new method which is useful to study convergences of certain random upper semicontinuous elements by taking advantages of some well-known results concerning random cadlag functions. The suggested method is applied in the paper to developed strong laws of large numbers.