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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 u 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 u 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 , Σ , μ , 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 , Σ , μ , 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 |
10 | 30 |
Three Basic Principles of Linear Analysis | 49 |
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A₁ additive set function algebra analytic arbitrary B-space B₁ ba(S Banach Borel sets ca(S Cauchy sequence closed unit sphere compact Hausdorff space compact operator complex numbers conditionally compact contains continuous functions convex set Corollary countably additive DEFINITION denote dense E₁ element equation equivalent exists f₁ finite dimensional function defined function f Hausdorff space Hence Hilbert space homeomorphism implies inequality integral isometric isomorphism K₁ L₁ L₁(S Lebesgue measure Lemma Let f linear map linear operator linear topological space Math measurable functions measure space metric space neighborhood non-negative non-zero normed linear space o-field o-finite open set operator topology positive measure space properties proved real numbers reflexive Riesz S₁ scalar semi-group sequentially compact Show subset subspace Suppose theory TM(S topological space u-integrable u-measurable uniformly valued function weak topology weakly compact weakly sequentially compact X₁ zero ΕΕΣ