Linear Operators: General theory |
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... union , or sum , of the sets a in A. This union is denoted by UA or a . The intersection , or product , of the sets a in A is the set of a € A = .... all a in A which are elements of every a € A. If A { a , b , c } we will sometimes ...
... union , or sum , of the sets a in A. This union is denoted by UA or a . The intersection , or product , of the sets a in A is the set of a € A = .... all a in A which are elements of every a € A. If A { a , b , c } we will sometimes ...
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... union of every one of its subfamilies , and the intersection of every one of its finite subfamilies . The pair ( X , t ) is called a topological space ; but sometimes ift is understood , we refer to X as a topological space . If T , T1 ...
... union of every one of its subfamilies , and the intersection of every one of its finite subfamilies . The pair ( X , t ) is called a topological space ; but sometimes ift is understood , we refer to X as a topological space . If T , T1 ...
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... union is in t . For an example of a finitely additive set function , let S = [ 0 , 1 ) and let be the family of intervals I = [ a , b ) , 0 ≤ a < b < 1 , with μ ( 1 ) = t b - a . We will ordinarily require that the domain of an ...
... union is in t . For an example of a finitely additive set function , let S = [ 0 , 1 ) and let be the family of intervals I = [ a , b ) , 0 ≤ a < b < 1 , with μ ( 1 ) = t b - a . We will ordinarily require that the domain of an ...
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