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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 setvalued probability useful in Bayesian inference is provided.doi:10.1214/aop/1176993455 fatcat:7znnhmymsna6jnn224cpja3dda