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Page 95
... values + ando . A positive set function is a real valued or extended real valued set function which has no negative values . 95 2 DEFINITION . A set function μ defined on a Integration and Set Functions Finitely Additive Set Functions.
... values + ando . A positive set function is a real valued or extended real valued set function which has no negative values . 95 2 DEFINITION . A set function μ defined on a Integration and Set Functions Finitely Additive Set Functions.
Page 119
... function f ( vector or extended real - valued ) which is defined only on the complement of a u - null set NCS . Then we say that f 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 f ( vector or extended real - valued ) which is defined only on the complement of a u - null set NCS . Then we say that f 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 L ( T , ΣT , 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 , ΣT , λ ) , 1 ≤ p < ∞ . For each s in S , F ( s ) is an equivalence class of functions , ...
Contents
Preliminary Concepts | 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 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 ergodic exists f₁ finite dimensional function defined function f 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-integrable u-measurable uniformly weak topology weakly compact weakly sequentially compact zero ΕΕΣ