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Page 103
... denote the set of rational points in S. For r = pq e R in lowest terms , we define F ( p / q ) = 1 / q , and set f ... denote the class of functions equivalent to ƒ ( i.e. all g such that ƒ — g is a u - null function ) , and let F ( S ...
... denote the set of rational points in S. For r = pq e R in lowest terms , we define F ( p / q ) = 1 / q , and set f ... denote the class of functions equivalent to ƒ ( i.e. all g such that ƒ — g is a u - null function ) , and let F ( S ...
Page 142
... denote a set in Σ , 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 * , let ...
... denote a set in Σ , 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 * , let ...
Page 469
... Denote the determinant whose columns are the vectors ā ( t ; x ) , ... f ( t ; x ) by Do ( t ; x ) and consider the ... denote the unit sphere in the space of variables x1 , Xi + 1 , ... , xn . Let at denote the positive square root { 1 ...
... Denote the determinant whose columns are the vectors ā ( t ; x ) , ... f ( t ; x ) by Do ( t ; x ) and consider the ... denote the unit sphere in the space of variables x1 , Xi + 1 , ... , xn . Let at denote the positive square root { 1 ...
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