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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 ... 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 ... established in the following theorem . Throughout this discus- sion of Hilbert space the conditions ( 1 ) ...
Page 608
... establishing this unification . However , it seems fair to state that it was F. Riesz who most fully revealed and ... established that the resolvent set is open , that the resolvent operator is analytic and indicated that , at least ...
... establishing this unification . However , it seems fair to state that it was F. Riesz who most fully revealed and ... established that the resolvent set is open , that the resolvent operator is analytic and indicated that , at least ...
Page 729
... established by G. D. Birkhoff [ 1 ] , who discussed measure preserving homeomorphisms of manifolds . The case of a finite measure space was treated by Khintchine [ 1 ] and the case of an infinite measure space by Stepanoff [ 1 ] . Some ...
... established by G. D. Birkhoff [ 1 ] , who discussed measure preserving homeomorphisms of manifolds . The case of a finite measure space was treated by Khintchine [ 1 ] and the case of an infinite measure space by Stepanoff [ 1 ] . Some ...
Contents
A Settheoretic Preliminaries | 1 |
B Topological Preliminaries | 10 |
Algebraic Preliminaries | 34 |
Copyright | |
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A₁ Acad additive set function algebra Amer analytic arbitrary B-space 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 exists f₁ finite dimensional function defined function f g₁ 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-measurable uniformly weak topology weakly compact weakly sequentially compact zero ΕΕΣ