Convergence of conditional expectations and strong laws of large numbers for multivalued random variables

Hiai, Fumio

doi:10.1090/S0002-9947-1985-0800254-X

Convergence of conditional expectations and strong laws of large numbers for multivalued random variables
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Trans. Amer. Math. Soc. 291 (1985), 613-627 Request permission

Abstract:

Fatou’s lemmas and Lebesgue’s convergence theorems are established for multivalued conditional expectations of random variables having values in the closed subsets of a separable Banach space. Strong laws of large numbers are also given for such multivalued random variables.

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Geometry and martingales in Banach spaces—Part

Independent increments