## Duality in Measure Theory |

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algebras approximation property arbitrary assertion follows associated Assume Banach Banach Spaces band belongs bounded set called Cauchy circled compact set containing continuous real functions continuous with respect converges Corollary countable deduce defined Definition denote disjoint dual duality E-complete Edited element endowed equal equicontinuous exists a finite exists a unique filter finite subset follows immediately fundamental solid subspace Hence increasing sequence induced isomorphism of vector Lemma let F Let Y,u,v linear map locally convex space measurable real function measures norm O-neighbourhood o-ring obvious polar set positive possesses Proceedings Proposition 3.1.1 prove real measures relation relatively compact Remark representation of x,M result seminorm sequence Supp Theorem Theory tion unital upper bounded vector lattice vector space VIII weakly weakly compact x'EE x'ou