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Page 4
... denotes the infimum of all numbers b with the property that only a finite set of numbers in A exceed b ; the de- finition of ... denote the least upper bound of F by sup F or lub F and the greatest lower bound of F by inf F or glb F. 4 ...
... denotes the infimum of all numbers b with the property that only a finite set of numbers in A exceed b ; the de- finition of ... denote the least upper bound of F by sup F or lub F and the greatest lower bound of F by inf F or glb F. 4 ...
Page 103
... denote the class of functions equivalent to f ( i.e. all g such that f - g is a u - null function ) , and let F ( S , E , u , X ) denote the set of all such sets [ f ] . If the following equations are used to define their left hand mem ...
... denote the class of functions equivalent to f ( i.e. all g such that f - g is a u - null function ) , and let F ( S , E , u , X ) denote the set of all such sets [ f ] . If the following equations are used to define their left hand mem ...
Page 142
... denote a set in 2 , the symbol M with or without subscripts will denote a set in for which v ( u , M ) = 0 , and N with or without subscripts will denote a subset of a set M. To see that the complement of a set EUN in E * is also in Σ ...
... denote a set in 2 , the symbol M with or without subscripts will denote a set in for which v ( u , M ) = 0 , and N with or without subscripts will denote a subset of a set M. To see that the complement of a set EUN in E * is also in Σ ...
Contents
B Topological Preliminaries | 10 |
Metric Spaces | 23 |
Product Spaces | 31 |
Copyright | |
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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