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Page 247
... establish the isometry when p 1 or . Q.E.D. 4. Hilbert Space = Of the infinite dimensional B - spaces , Hilbert space is the most ... established in the following theorem . Throughout this discus- sion of Hilbert space the conditions ( 1 ) ...
... establish the isometry when p 1 or . Q.E.D. 4. Hilbert Space = Of the infinite dimensional B - spaces , Hilbert space is the most ... established in the following theorem . Throughout this discus- sion of Hilbert space the conditions ( 1 ) ...
Page 403
... establish an integration theory ( finitely additive ) for functions on H. It turns out , however , that this integration theory is not sufficiently inclusive for the customary applications of the Gauss integral . Hence , it is well to ...
... establish an integration theory ( finitely additive ) for functions on H. It turns out , however , that this integration theory is not sufficiently inclusive for the customary applications of the Gauss integral . Hence , it is well to ...
Page 463
... established the equivalence of these types of closure without any separability assumptions . In a similar vein , Krein and Smulian [ 1 ] introduced a definition of a regularly convex set in X * . It is not difficult to establish that ...
... established the equivalence of these types of closure without any separability assumptions . In a similar vein , Krein and Smulian [ 1 ] introduced a definition of a regularly convex set in X * . It is not difficult to establish that ...
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