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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 , complex function , etc ... set function μ defined on a 95 Integration and 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 , complex function , etc ... set function μ defined on a 95 Integration and 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 S = S1 ... S2 containing & such that μ ( E ) ... 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 S = S1 ... S2 containing & such that μ ( E ) ... set 184 III.11.1 III . INTEGRATION AND SET FUNCTIONS.
Contents
B Topological Preliminaries | 10 |
Metric Spaces | 23 |
Product Spaces | 31 |
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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 Doklady Akad Duke Math E₁ elements ergodic exists extension f₁ function defined function f Hausdorff space Hence Hilbert space homomorphism inequality integral L₁ L₁(S Lebesgue Lemma Let f linear functional linear map linear operator linear topological space measurable functions measure space metric space Nauk SSSR N. S. neighborhood non-negative normed linear space o-field open set operator topology positive measure space Proc PROOF properties proved real numbers reflexive Riesz Russian S₁ scalar semi-group sequentially compact Show subset subspace Suppose theory topological space u-integrable u-measurable u-null uniformly unit sphere valued function vector space weakly compact zero ΕΕΣ