Linear Operators: General theory |
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Page 95
... values + and -∞ . A positive set function is a real valued or extended real valued set function which has no negative values . 2 DEFINITION . A set function u defined on a 95 Integration and Set Functions 35 Finitely Additive Set ...
... values + and -∞ . A positive set function is a real valued or extended real valued set function which has no negative values . 2 DEFINITION . A set function u defined on a 95 Integration and Set Functions 35 Finitely Additive Set ...
Page 119
... function ƒ ( vector or extended real - valued ) which is defined only on the complement of a u - null set NCS . Then we say that ƒ is u - measurable if the function g defined by g ( s ) = f ( s ) if s ¢ N , g ( s ) = 0 if s e N , is u ...
... function ƒ ( vector or extended real - valued ) which is defined only on the complement of a u - null set NCS . Then we say that ƒ is u - measurable if the function g defined by g ( s ) = f ( s ) if s ¢ N , g ( s ) = 0 if s e N , is u ...
Page 196
... valued integrals . In the application of the theory of vector valued integrals to concrete problems such as the ... function whose values are in L2 ( T , ET , λ ) , 1 ≤ p < ∞ . For each s in S , F ( s ) is an equivalence class of functions ...
... valued integrals . In the application of the theory of vector valued integrals to concrete problems such as the ... function whose values are in L2 ( T , ET , λ ) , 1 ≤ p < ∞ . For each s in S , F ( s ) is an equivalence class of functions ...
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