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absolutely convex absolutely countably additive additive and bounded adjoint Banach space BDS holds bounded additive function bounded in total bounded subsets Cauchy classical result CLCS closed unit ball compact subsets continuous linear map convex cover Corollary 4.7 countable family countably compact denote disjoint measurable sets dual of M(R extends f e M(R finer follows from Theorem Hausdorff Hence implies increasing sequence infrabarrelled Lemma locally convex spaces M(IP Mackey space Mackey topology neighborhood norm on M(R o-ring o(M(R)',M(R)")-relative compactness o(W,W')-relatively compact pairwise disjoint measurable positive integers Proposition 7.3 relatively compact scalar measure sequence of measurable sequentially compact strong topology subsets of M(R sup norm t-bounded T-equicontinuous subsets Theorem 6.8 topology of uniform topology on M(R total variation norm uaca uniform convergence uniformly absolutely countably uniformly countably additive unit point measure universal measure vector measure vector space weak topology