Laws of Large Numbers for Uncorrelated Set-Valued Random Variables

Abstract: As the extension of uncorrelated single-valued random variables, set-valued case is studied in this paper. When the underlying space is of finite dimension, by using the support function, We shall prove the weak and strong laws of large numbers for uncorrelated set-valued random variables in the sense of Hausdorff metric $d_H$. Our results generalize weak and strong laws of large numbers for independent identically distributed or independent set-valued random variables.