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Page 311
... isomorphism of B ( S , E ) with C ( S1 ) where S1 is a particular compact Hausdorff space . We shall now investigate what properties the existence of this isomorphism implies for S1 and investigate in more detail the isomorphism of ba ...
... isomorphism of B ( S , E ) with C ( S1 ) where S1 is a particular compact Hausdorff space . We shall now investigate what properties the existence of this isomorphism implies for S1 and investigate in more detail the isomorphism of ba ...
Page 312
... isomorphic with C ( S1 ) . Then the space S1 is uniquely de- termined to within a homeomorphism and is totally disconnected . The correspondence XE → XE , establishes an isomorphism t of the field Σ onto of all open and closed sets in ...
... isomorphic with C ( S1 ) . Then the space S1 is uniquely de- termined to within a homeomorphism and is totally disconnected . The correspondence XE → XE , establishes an isomorphism t of the field Σ onto of all open and closed sets in ...
Page 313
... isomorphism of ba ( S1 , E1 ) onto ca ( S1 , E2 ) . 1 ( c ) If E1 is in Σ1 then v ( μ1 , E1 ) = v ( U ( μ1 ) , E1 ) for all ba ( S1 , 1 ) . μ1 in PROOF . Recalling that is an isomorphism of Σ onto 1 , it is clear that the mapping T is ...
... isomorphism of ba ( S1 , E1 ) onto ca ( S1 , E2 ) . 1 ( c ) If E1 is in Σ1 then v ( μ1 , E1 ) = v ( U ( μ1 ) , E1 ) for all ba ( S1 , 1 ) . μ1 in PROOF . Recalling that is an isomorphism of Σ onto 1 , it is clear that the mapping T is ...
Contents
8 | 28 |
Algebraic Preliminaries | 34 |
Three Basic Principles of Linear Analysis | 49 |
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A₁ additive set function algebra Amer analytic arbitrary B-space ba(S Banach Borel sets ca(S Cauchy sequence compact Hausdorff space compact operator complex numbers contains continuous functions converges convex set Corollary countably additive DEFINITION dense differential disjoint Doklady Akad E₁ element equation exists f₁ finite dimensional function defined function f Hausdorff space Hence Hilbert space homeomorphism implies inequality integral isometric isomorphism L₁ L₁(S Lebesgue Lemma Let f linear map linear operator linear topological space Math measurable functions measure space metric space Nauk SSSR N. S. neighborhood non-negative normed linear space o-field o-finite open set operator topology positive measure space Proc PROOF properties proved real numbers Riesz S₁ scalar semi-group sequentially compact Show subset subspace Suppose theory TM(S topological space u-integrable u-measurable uniformly weak topology weakly compact weakly sequentially compact zero ΕΕΣ