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Page 81
... give those theorems or to give generalizations of some theorems of Saks II.5 81 NOTES AND REMARKS.
... give those theorems or to give generalizations of some theorems of Saks II.5 81 NOTES AND REMARKS.
Page 82
... give a very simple proof of the uniform boundedness theorem for B - spaces . Bourbaki [ 3 ] has demonstrated that Theorem 1.17 remains valid in a certain class of locally convex topological linear spaces . ( See also Dieudonné and ...
... give a very simple proof of the uniform boundedness theorem for B - spaces . Bourbaki [ 3 ] has demonstrated that Theorem 1.17 remains valid in a certain class of locally convex topological linear spaces . ( See also Dieudonné and ...
Page 337
... give answers valid for the space BV ( I ) to many other of the ques- tions asked in Section 1. We leave the details to the reader as an exer- cise . It was shown in Chapter III.5 ( cf. the discussion following Lemma III.5.16 ) that if f ...
... give answers valid for the space BV ( I ) to many other of the ques- tions asked in Section 1. We leave the details to the reader as an exer- cise . It was shown in Chapter III.5 ( cf. the discussion following Lemma III.5.16 ) that if f ...
Contents
Exercises | 9 |
Definitions and Basic Properties | 13 |
Metric Spaces | 19 |
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 closed sets compact Hausdorff space compact operator complex numbers contains continuous functions continuous linear converges convex set Corollary countably additive DEFINITION denote dense disjoint Doklady Akad E₁ elements ergodic exists f₁ finite number follows function defined function f Hausdorff space Hence Hilbert space homomorphism 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 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 Theorem theory topological space u-integrable u-measurable u-null uniformly unit sphere vector space weakly compact zero ΕΕΣ