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Page 103
... denote the class of functions equivalent to ƒ ( i.e. all g such that f - g is a u - null function ) , and let F ( S , Z , 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 ƒ ( i.e. all g such that f - g is a u - null function ) , and let F ( S , Z , 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 * is also in 2 ...
... 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 * is also in 2 ...
Page 469
... denote the unit sphere in the space of variables a , ... , Xi - 19 Xi + 1 , ... , xn . Let at denote the positive square root { 1- ( x + ... + æ12 + æ12 + ... + 2 ) } 1/2 , and a denote the corresponding negative + x¿ - 1 + i + 1 square ...
... denote the unit sphere in the space of variables a , ... , Xi - 19 Xi + 1 , ... , xn . Let at denote the positive square root { 1- ( x + ... + æ12 + æ12 + ... + 2 ) } 1/2 , and a denote the corresponding negative + x¿ - 1 + i + 1 square ...
Contents
8 | 28 |
Algebraic Preliminaries | 34 |
Three Basic Principles of Linear Analysis | 49 |
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A₁ additive set function algebra Amer analytic arbitrary B-space ba(S Banach Borel sets ca(S Cauchy sequence compact Hausdorff space compact operator complex numbers contains continuous functions converges convex set Corollary countably additive DEFINITION dense differential disjoint Doklady Akad E₁ element equation exists f₁ finite dimensional function defined function f Hausdorff space Hence Hilbert space homeomorphism implies inequality integral isometric isomorphism L₁ L₁(S Lebesgue Lemma Let f linear map linear operator linear topological space Math measurable functions measure space metric space Nauk SSSR N. S. neighborhood non-negative normed linear space o-field o-finite open set operator topology positive measure space Proc PROOF properties proved real numbers Riesz S₁ scalar semi-group sequentially compact Show subset subspace Suppose theory TM(S topological space u-integrable u-measurable uniformly weak topology weakly compact weakly sequentially compact zero ΕΕΣ