Linear Operators: General theory |
From inside the book
Results 1-3 of 85
Page 132
... extension theorem of Hahn and similar extension theorems , of importance in later applications , will be discussed in this section . Finally , it is shown how the extension theorems may be used to construct the classical measures of ...
... extension theorem of Hahn and similar extension theorems , of importance in later applications , will be discussed in this section . Finally , it is shown how the extension theorems may be used to construct the classical measures of ...
Page 136
... extension of μ to the o - field E determined by 2. Suppose that μ1 is another such extension . If is o - finite on Σ to prove the uniqueness of the extension , it will suffice to show that μ ( E ) = μ1 ( E ) for every set E in 2 ...
... extension of μ to the o - field E determined by 2. Suppose that μ1 is another such extension . If is o - finite on Σ to prove the uniqueness of the extension , it will suffice to show that μ ( E ) = μ1 ( E ) for every set E in 2 ...
Page 143
... extension of μ . The o - field Σ * is known as the Lebesgue extension ( relative to μ ) of the o - field Σ , and the measure space ( S , Σ * , μ ) is the Lebesgue extension of the measure space ( S , E , μ ) . Expressions such as μ ...
... extension of μ . The o - field Σ * is known as the Lebesgue extension ( relative to μ ) of the o - field Σ , and the measure space ( S , Σ * , μ ) is the Lebesgue extension of the measure space ( S , E , μ ) . Expressions such as μ ...
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