Linear Operators: General theory |
From inside the book
Results 1-3 of 62
Page 106
... simple functions . If for every E in E with v ( u , E ) < ∞ , the product Xef of f with the characteristic function ... functions are M ( S , Σ , μ , X ) , M ( S , Σ , μ ) , M ( S ) and symbols besides TM ( S ) for the set of totally ...
... simple functions . If for every E in E with v ( u , E ) < ∞ , the product Xef of f with the characteristic function ... functions are M ( S , Σ , μ , X ) , M ( S , Σ , μ ) , M ( S ) and symbols besides TM ( S ) for the set of totally ...
Page 108
... simple function " and " u - integrable simple function " will be used interchan- geably . For an Ee the integral over E of a u - integrable simple func- tion h is defined by the equation [ _h ( s ) u ( ds ) = √ f ( s ) u ( ds ) S E E ...
... simple function " and " u - integrable simple function " will be used interchan- geably . For an Ee the integral over E of a u - integrable simple func- tion h is defined by the equation [ _h ( s ) u ( ds ) = √ f ( s ) u ( ds ) S E E ...
Page 322
... function ƒ defined on S is u - simple if it is a finite linear combination of characteristic functions of sets in Σ * ; this is evidently the case if and only if ƒ is 2 - simple . It follows from Corollaries III.6.13 and III.6.14 that ...
... function ƒ defined on S is u - simple if it is a finite linear combination of characteristic functions of sets in Σ * ; this is evidently the case if and only if ƒ is 2 - simple . It follows from Corollaries III.6.13 and III.6.14 that ...
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