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Page 11
... LEMMA . If ẞ is a family of subsets of X , and if τ is the family of all unions of subfamilies of B , then r is a topology if and only if ( i ) for every pair U , V e ẞ and xe UV there is a We ß , such that xe WCUV , and ( ii ) X = Uẞ ...
... LEMMA . If ẞ is a family of subsets of X , and if τ is the family of all unions of subfamilies of B , then r is a topology if and only if ( i ) for every pair U , V e ẞ and xe UV there is a We ß , such that xe WCUV , and ( ii ) X = Uẞ ...
Page 410
... lemma is an obvious consequence of Definition 1 . 2 LEMMA . The intersection of an arbitrary family of convex subsets of the linear space X is convex . As examples of convex subsets of X , we note the subspaces of X , and the subsets of ...
... lemma is an obvious consequence of Definition 1 . 2 LEMMA . The intersection of an arbitrary family of convex subsets of the linear space X is convex . As examples of convex subsets of X , we note the subspaces of X , and the subsets of ...
Page 700
... lemma is known to be true for an integer k it is also true for any integer m≤k . Thus , to prove the lemma , it will suffice to show that it is true if k is even . If k 1 the lemma has al- ready been proved ( Lemma 6 ) . We shall thus ...
... lemma is known to be true for an integer k it is also true for any integer m≤k . Thus , to prove the lemma , it will suffice to show that it is true if k is even . If k 1 the lemma has al- ready been proved ( Lemma 6 ) . We shall thus ...
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