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Page 95
Nelson Dunford, Jacob T. Schwartz. CHAPTER III Integration and Set Functions 1. Finitely Additive Set Functions In contrast to the terms real ... function u defined on a 95 Integration and Set Functions 35 Finitely Additive Set Functions.
Nelson Dunford, Jacob T. Schwartz. CHAPTER III Integration and Set Functions 1. Finitely Additive Set Functions In contrast to the terms real ... function u defined on a 95 Integration and Set Functions 35 Finitely Additive Set Functions.
Page 96
... variation of μ . The set function v ( u ) is defined so as to be equal to u if u itself is non - negative , to be additive if u is additive , and to be bounded if u is bounded . The 96 III.1.2 III . INTEGRATION AND SET FUNCTIONS.
... variation of μ . The set function v ( u ) is defined so as to be equal to u if u itself is non - negative , to be additive if u is additive , and to be bounded if u is bounded . The 96 III.1.2 III . INTEGRATION AND SET FUNCTIONS.
Page 131
... set functions defined on a field Σ . Then 2 is said to be continuous with respect to μ or simply u - continuous , if lim 2 ( E ) = v ( μ , E ) →→ 0 0 . The function ¿ is said to be u - singular if there is a set Ee such that v ( μ ...
... set functions defined on a field Σ . Then 2 is said to be continuous with respect to μ or simply u - continuous , if lim 2 ( E ) = v ( μ , E ) →→ 0 0 . The function ¿ is said to be u - singular if there is a set Ee such that v ( μ ...
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