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Page 95
... valued function and ƒ a vector ( or scalar ) valued function . Thus , even if the integration process is defined with respect to a scalar valued set function μ , the resulting ... function u defined on a 95 Integration and Set Functions.
... valued function and ƒ a vector ( or scalar ) valued function . Thus , even if the integration process is defined with respect to a scalar valued set function μ , the resulting ... function u defined on a 95 Integration and Set Functions.
Page 119
... function f ( vector or extended real - valued ) which is defined only on the complement of a μ - 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 se N , is u ...
... function f ( vector or extended real - valued ) which is defined only on the complement of a μ - 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 se 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 L „ ( T , Σr , 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 L „ ( T , Σr , λ ) , 1 ≤ p < ∞ . For each s in S , F ( s ) is an equivalence class of functions ...
Contents
8 | 28 |
Algebraic Preliminaries | 34 |
Three Basic Principles of Linear Analysis | 49 |
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A₁ additive set function algebra Amer analytic arbitrary B-space ba(S Banach Borel sets ca(S Cauchy sequence compact Hausdorff space compact operator complex numbers contains continuous functions converges convex set Corollary countably additive DEFINITION dense differential disjoint Doklady Akad E₁ element equation exists f₁ finite dimensional function defined function f Hausdorff space Hence Hilbert space homeomorphism implies inequality integral isometric isomorphism L₁ L₁(S Lebesgue Lemma Let f linear map linear operator linear topological space Math measurable functions measure space metric space Nauk SSSR N. S. neighborhood non-negative normed linear space o-field o-finite open set operator topology positive measure space Proc PROOF properties proved real numbers Riesz S₁ scalar semi-group sequentially compact Show subset subspace Suppose theory TM(S topological space u-integrable u-measurable uniformly weak topology weakly compact weakly sequentially compact zero ΕΕΣ