Linear Operators: General theory |
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Page 3
... indices . If B is a collection of sets , the union f ( A ) will sometimes be written as Uba , and f ( A ) , as ba α αελ aεA A relation in ( or on ) a set A is a collection r of ordered pairs [ x , y ] of elements of A. It is customary ...
... indices . If B is a collection of sets , the union f ( A ) will sometimes be written as Uba , and f ( A ) , as ba α αελ aεA A relation in ( or on ) a set A is a collection r of ordered pairs [ x , y ] of elements of A. It is customary ...
Page 46
... indices 1 ≤ j < < i , ≤n . Similarly , det ( a ,, ) may be calculated in terms of ele- ments of the j1 , . . . , j , th columns by summing over all sets of p indices 1≤į < ... < i , ≤n . In case p = 1 the Laplace expansion reduces ...
... indices 1 ≤ j < < i , ≤n . Similarly , det ( a ,, ) may be calculated in terms of ele- ments of the j1 , . . . , j , th columns by summing over all sets of p indices 1≤į < ... < i , ≤n . In case p = 1 the Laplace expansion reduces ...
Page 162
... indices and all finite families of disjoint sets { E } in Σ whose union is E. It will first be shown that μ is additive on E. Let E , F be disjoint sets in Σ and let > 0 be arbitrary . Let EU F be partitioned into disjoint sets A1 ,. Am ...
... indices and all finite families of disjoint sets { E } in Σ whose union is E. It will first be shown that μ is additive on E. Let E , F be disjoint sets in Σ and let > 0 be arbitrary . Let EU F be partitioned into disjoint sets A1 ,. Am ...
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