Linear Operators: General theory |
From inside the book
Results 1-3 of 72
Page 137
... regular additive complex or extended real valued set function on a field is regular . Moreover , the positive and negative variations of a bounded regular real valued additive set function are also regular . PROOF . If μ is a regular ...
... regular additive complex or extended real valued set function on a field is regular . Moreover , the positive and negative variations of a bounded regular real valued additive set function are also regular . PROOF . If μ is a regular ...
Page 170
... regular and defined on the field of Borel sets in S. Show that if X is separable , the set of continuous functions in TM ( S , E , u , X ) is dense in TM ( S , E , u , X ) . Show that for 1 ≤ p < ∞o , the set of con- tinuous functions ...
... regular and defined on the field of Borel sets in S. Show that if X is separable , the set of continuous functions in TM ( S , E , u , X ) is dense in TM ( S , E , u , X ) . Show that for 1 ≤ p < ∞o , the set of con- tinuous functions ...
Page 853
... Regular closure , ( 462-463 ) Regular convexity , ( 462-463 ) Regular element in a ring , ( 40 ) Regular method of summability , II.4.35 ( 75 ) Regular set function . ( See also Set function ) additional properties , III.9.19-22 ( 170 ) ...
... Regular closure , ( 462-463 ) Regular convexity , ( 462-463 ) Regular element in a ring , ( 40 ) Regular method of summability , II.4.35 ( 75 ) Regular set function . ( See also Set function ) additional properties , III.9.19-22 ( 170 ) ...
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