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Let τλ be the topology of convergence locally in measure on L1=L1(λ) and P be the Yosida–Hewitt projection from L1∗∗ onto L1. We characterize convex, τλ-compact subsets C of L1 as precisely those for which P is a compactness preserving map from C¯w∗ with the weak∗-topology to C with the τλ-topology. We further show that a convex, τλ-closed, L1-norm bounded subset C of L1 is a Schur set if and only...
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