Summary
Let {C n } be a sequence of closed convex subsets in a Hilbert space H. We prove that the prediction sequence {p(x¦Cn)} converges for every xεH if and only if s-lim C n exists and is not empty. We further show the relation between the limit of closed convex sets and the one of σ-subfields in probability measure spaces.
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Tsukada, M. Convergence of closed convex sets and σ-fields. Z. Wahrscheinlichkeitstheorie verw Gebiete 62, 137–146 (1983). https://doi.org/10.1007/BF00532167
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DOI: https://doi.org/10.1007/BF00532167