Linear Operators: General theory |
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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 Σ of Borel sets in S. Show that if X is separable , the set of continuous functions in TM ( S , E , μ , X ) is dense in TM ( S , Σ , u , X ) . Show that for 1 ≤ p < ∞ , the set of con- tinuous ...
... regular and defined on the field Σ of Borel sets in S. Show that if X is separable , the set of continuous functions in TM ( S , E , μ , X ) is dense in TM ( S , Σ , u , X ) . Show that for 1 ≤ p < ∞ , the set of con- tinuous ...
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 |
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A₁ Acad additive set function algebra Amer analytic arbitrary B-space B₁ ba(S Banach spaces Borel sets Cauchy sequence compact operator complex numbers contains continuous functions continuous linear converges convex set Corollary countably additive DEFINITION denote dense differential equations disjoint Doklady Akad domain E₁ element exists f₁ finite dimensional finite number function defined function f Hausdorff space Hence Hilbert space homeomorphism inequality integral L₁ L₁(S Lebesgue Lemma Let f linear functional linear map linear operator linear topological space measurable function measure space metric space Nauk SSSR N. S. neighborhood non-negative o-field open set operator topology positive measure space Proc PROOF proved real numbers Riesz Russian S₁ scalar semi-group sequentially compact Show spectral strong operator topology subset subspace Suppose T₁ theory topological space u-integrable u-measurable uniformly unit sphere valued function weakly compact zero ΕΕΣ