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An almost independent set-valued process on a Loeb product space is shown to be representable as the closure of a sequence of its selections which are almost independent themselves. This provides a Castaing type representation in terms of independent correspondences. Different definitions of independence for correspondences in the literature are also unified in a general setting.doi:10.1090/s0002-9939-00-05652-5 fatcat:hyejjyxqbbgt3okovxbpeunoeu