Linear Operators: General theory |
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Page 241
... Remark . In Chapter III the space L , ( S , Σ , μ ) was defined without the assumption that μ is non - negative . The space L , ( S , E , u ) is , in any case , the same as the space L , ( S , Σ , v ( μ ) ) and the variation v ( μ ) is ...
... Remark . In Chapter III the space L , ( S , Σ , μ ) was defined without the assumption that μ is non - negative . The space L , ( S , E , u ) is , in any case , the same as the space L , ( S , Σ , v ( μ ) ) and the variation v ( μ ) is ...
Page 838
... remarks concerning , ( 383 ) Ascoli - Arzelà theorem , on compact- ness of continuous functions , IV.6.7 ( 266 ) remarks concerning , ( 382 ) Atom , in a measure space , IV.9.6 ( 308 ) Automorphisms , in groups , ( 35 ) B B - space ( or ...
... remarks concerning , ( 383 ) Ascoli - Arzelà theorem , on compact- ness of continuous functions , IV.6.7 ( 266 ) remarks concerning , ( 382 ) Atom , in a measure space , IV.9.6 ( 308 ) Automorphisms , in groups , ( 35 ) B B - space ( or ...
Page 844
... remarks on , ( 728-730 ) Essential least upper bound , definition III.1.11 ( 100–101 ) Essential singularity , definition ... remark on , ( 88 ) Fatou theorem , on limits and integrals , III.6.19 ( 152 ) , III.9.35 ( 172 ) Field , in ...
... remarks on , ( 728-730 ) Essential least upper bound , definition III.1.11 ( 100–101 ) Essential singularity , definition ... remark on , ( 88 ) Fatou theorem , on limits and integrals , III.6.19 ( 152 ) , III.9.35 ( 172 ) Field , in ...
Contents
A Settheoretic Preliminaries | 1 |
B Topological Preliminaries | 10 |
Algebraic Preliminaries | 34 |
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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