Linear Operators: General theory |
From inside the book
Results 1-3 of 83
Page 171
... Suppose that every continuous function is μ - measurable . Show that E * contains every Borel set . 24 Suppose that S is a compact topological space , with the property that for every covering of S by a finite number of open sets G1 ...
... Suppose that every continuous function is μ - measurable . Show that E * contains every Borel set . 24 Suppose that S is a compact topological space , with the property that for every covering of S by a finite number of open sets G1 ...
Page 225
... suppose that B consists of a finite collection of disjoint closed rectifiable Jordan curves ; that is , we suppose that B can be decomposed into the union B = B1UBU ... UB of dis- joint closed sets B , in such a way that each B , is a ...
... suppose that B consists of a finite collection of disjoint closed rectifiable Jordan curves ; that is , we suppose that B can be decomposed into the union B = B1UBU ... UB of dis- joint closed sets B , in such a way that each B , is a ...
Page 360
... Suppose that 0≤x≤27 ( i ) ( Snf ) ( x ) → f ( x ) uniformly in x for ƒ in AC . ( ii ) The convergence of Sf is localized . Show that for any ƒ in CBV , ( Sf ) ( x ) f ( x ) uniformly in a . → 24 Suppose ( i ) , ( ii ) of the last ...
... Suppose that 0≤x≤27 ( i ) ( Snf ) ( x ) → f ( x ) uniformly in x for ƒ in AC . ( ii ) The convergence of Sf is localized . Show that for any ƒ in CBV , ( Sf ) ( x ) f ( x ) uniformly in a . → 24 Suppose ( i ) , ( ii ) of the last ...
Contents
A Settheoretic Preliminaries | 1 |
B Topological Preliminaries | 10 |
Algebraic Preliminaries | 34 |
Copyright | |
59 other sections not shown
Other editions - View all
Common terms and phrases
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