Linear Operators: General theory |
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Page 770
... Haar's measure . Proc . Imp . Acad . Tokyo 14,27-31 ( 1938 ) . A proof of the uniqueness of Haar's measure . Ann . of Math . ( 2 ) 49 , 225–226 ( 1948 ) . On the uniform ergodic theorem concerning real linear operations . Jap . J. Math ...
... Haar's measure . Proc . Imp . Acad . Tokyo 14,27-31 ( 1938 ) . A proof of the uniqueness of Haar's measure . Ann . of Math . ( 2 ) 49 , 225–226 ( 1948 ) . On the uniform ergodic theorem concerning real linear operations . Jap . J. Math ...
Page 782
... Haar measure . Ann . of Math . ( 2 ) 46 , 348-355 ( 1945 ) . 5 . 4. Haar measure in uniform structures . Duke Math . J. 16 , 193-208 ( 1949 ) . On the representation of o - complete Boolean algebras . Bull . Amer . Math . Soc . 53 , 757 ...
... Haar measure . Ann . of Math . ( 2 ) 46 , 348-355 ( 1945 ) . 5 . 4. Haar measure in uniform structures . Duke Math . J. 16 , 193-208 ( 1949 ) . On the representation of o - complete Boolean algebras . Bull . Amer . Math . Soc . 53 , 757 ...
Page 801
... Haar's measure . Doklady Akad . Nauk SSSR ( N. S. ) 34 , 211-214 ( 1942 ) . Positive definite functions on commutative groups with an invariant measure . Doklady Akad . Nauk SSSR ( N. S. ) 28 , 296–300 ( 1940 ) . Ramaswami , V. 1 ...
... Haar's measure . Doklady Akad . Nauk SSSR ( N. S. ) 34 , 211-214 ( 1942 ) . Positive definite functions on commutative groups with an invariant measure . Doklady Akad . Nauk SSSR ( N. S. ) 28 , 296–300 ( 1940 ) . Ramaswami , V. 1 ...
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