Linear Operators: General theory |
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Page 95
... function , complex function , etc. , where the adjectives real and complex refer to the range of the func- tion , the term set function is commonly used in ... set & , if 95 Integration and Set Functions 95 35 Finitely Additive Set Functions.
... function , complex function , etc. , where the adjectives real and complex refer to the range of the func- tion , the term set function is commonly used in ... set & , if 95 Integration and Set Functions 95 35 Finitely Additive Set Functions.
Page 96
Nelson Dunford, Jacob T. Schwartz. If I contains the veid ༡ set & , if μcd ) = 0 , and if 2 DEFINITION . A set function u defined on a family τ of sets is said to be additive or finitely additive up ) = 0 and μ ( А1 ̄ Ã „ . . . U An ) ...
Nelson Dunford, Jacob T. Schwartz. If I contains the veid ༡ set & , if μcd ) = 0 , and if 2 DEFINITION . A set function u defined on a family τ of sets is said to be additive or finitely additive up ) = 0 and μ ( А1 ̄ Ã „ . . . U An ) ...
Page 184
... function defined on a field E of subsets of a set S. Then there is a unique additive set function μ defined on the smallest field Σ in S1 ... Sn containing & such that μ ( E ) ... set 184 III.11.1 III . INTEGRATION AND SET FUNCTIONS.
... function defined on a field E of subsets of a set S. Then there is a unique additive set function μ defined on the smallest field Σ in S1 ... Sn containing & such that μ ( E ) ... set 184 III.11.1 III . INTEGRATION AND SET 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 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