In this paper we define the expected value of a random vector with respect to a set-valued probability measure. The concepts of independent and identically distributed random vectors are appropriately defined, and a strong law of large numbers is derived in this setting. Finally, an example of a set-valued probability useful in Bayesian inference is provided.
"Strong Law of Large Numbers with Respect to a Set-Valued Probability Measure." Ann. Probab. 11 (4) 1051 - 1054, November, 1983. https://doi.org/10.1214/aop/1176993455