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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 XEZE , establishes an isomorphism r of the field Σ onto the field of all open and closed ...
... isomorphic with C ( S1 ) . Then the space S1 is uniquely de- termined to within a homeomorphism and is totally disconnected . The correspondence XEZE , establishes an isomorphism r of the field Σ onto the field of all open and closed ...
Page 313
... isomorphism of ba ( S1 , E1 ) onto ca ( S1 . 22 ) . ( c ) If E is in Σ1 then v ( μ1 , E1 ) = v ( U ( μ1 ) , E1 ) for all M1 in ba ( S1 , 21 ) . PROOF . Recalling that 7 is an isomorphism of Σ onto E1 , it is clear that the mapping T is ...
... isomorphism of ba ( S1 , E1 ) onto ca ( S1 . 22 ) . ( c ) If E is in Σ1 then v ( μ1 , E1 ) = v ( U ( μ1 ) , E1 ) for all M1 in ba ( S1 , 21 ) . PROOF . Recalling that 7 is an isomorphism of Σ onto E1 , it is clear that the mapping T is ...
Contents
Preliminary Concepts | 1 |
B Topological Preliminaries | 10 |
Algebraic Preliminaries | 34 |
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A₁ Acad additive set function algebra Amer analytic arbitrary B-space B₁ ba(S Banach spaces Borel sets ca(S Cauchy sequence compact Hausdorff space compact operator complex numbers contains continuous functions converges convex set Corollary countably additive DEFINITION dense disjoint Doklady Akad E₁ element ergodic exists f₁ finite dimensional function defined function f Hausdorff space Hence Hilbert space homeomorphism implies inequality integral isometric isomorphism K₁ L₁ L₁(S Lebesgue Lemma Let f linear manifold linear map linear operator linear topological space measurable functions measure space metric space Nauk SSSR N. S. neighborhood non-negative o-field o-finite open set operator topology positive measure space Proc PROOF properties proved real numbers reflexive Riesz S₁ scalar semi-group sequentially compact Show subset subspace Suppose theory topological space u-integrable u-measurable uniformly weak topology weakly compact weakly sequentially compact zero ΕΕΣ