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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 ... set function μ defined on a Integration and Set Functions 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 ... set function μ defined on a Integration and Set Functions Finitely Additive Set Functions.
Page 96
... variation of μ . The set function v ( μ ) is defined so as to be equal to u if u itself is non - negative , to be additive if u is additive , μ 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 ( μ ) is defined so as to be equal to u if u itself is non - negative , to be additive if u is additive , μ and to be bounded if u is bounded . The 96 III.1.2 III . INTEGRATION AND SET FUNCTIONS.
Page 184
... function defined on a field Σ ; of subsets of a set S. Then there is a unique additive set function μ defined on the smallest field Σ in S1 ... S containing & such that μ ( E ) = - 1 μ ... set 184 III.11.1 III . INTEGRATION AND SET FUNCTIONS.
... function defined on a field Σ ; of subsets of a set S. Then there is a unique additive set function μ defined on the smallest field Σ in S1 ... S containing & such that μ ( E ) = - 1 μ ... set 184 III.11.1 III . INTEGRATION AND SET 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