Linear Operators: General theory |
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Page 3
... restriction of ƒ if the domain of ƒ contains the domain of g , and f ( x ) = g ( x ) for x in the domain of g . The restriction of a function f to a subset A of its domain is sometimes denoted by f | A . If ƒ : A → B , and for each be ...
... restriction of ƒ if the domain of ƒ contains the domain of g , and f ( x ) = g ( x ) for x in the domain of g . The restriction of a function f to a subset A of its domain is sometimes denoted by f | A . If ƒ : A → B , and for each be ...
Page 101
... restriction of f to S - N is bounded , then f is said to be μ - essentially bounded or simply essentially bounded . The quantity inf sup | f ( s ) , N SES - N where N ranges over the μ - null subsets of S is called the u - essential ...
... restriction of f to S - N is bounded , then f is said to be μ - essentially bounded or simply essentially bounded . The quantity inf sup | f ( s ) , N SES - N where N ranges over the μ - null subsets of S is called the u - essential ...
Page 166
... restriction of μ to a subfield of Σ there is an- other type of restriction of common occurrence in integration theory . In the following discussion of this other type of restriction it is not necessary to assume that μ is non - negative ...
... restriction of μ to a subfield of Σ there is an- other type of restriction of common occurrence in integration theory . In the following discussion of this other type of restriction it is not necessary to assume that μ is non - negative ...
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