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Page 81
... Theorems 1.17 and 1.18 for B - spaces and gave [ 7 ] theorems related to these and the condensation theorem just mentioned for complete metric groups . ( See also Banach [ 1 ; Chap . 1 ] . ) The extension of Theorems 1.11 and 1.13 to F ...
... Theorems 1.17 and 1.18 for B - spaces and gave [ 7 ] theorems related to these and the condensation theorem just mentioned for complete metric groups . ( See also Banach [ 1 ; Chap . 1 ] . ) The extension of Theorems 1.11 and 1.13 to F ...
Page 82
Nelson Dunford, Jacob T. Schwartz. theorems or to give generalizations of some theorems of Saks [ 2 , 3 ] on sequences ... theorem of the condensation type where the double sequence of operators also de- pends on a parameter in a complete ...
Nelson Dunford, Jacob T. Schwartz. theorems or to give generalizations of some theorems of Saks [ 2 , 3 ] on sequences ... theorem of the condensation type where the double sequence of operators also de- pends on a parameter in a complete ...
Page 729
... theorems of the mean type , but in which other methods of summation replace the ( C , 1 ) -method ordinarily used , are proved by Cohen [ 2 ] , Hille [ 1 ; Chap . 14 ] and Phillips [ 4 ] . Pointwise ergodic theorem . This theorem was ...
... theorems of the mean type , but in which other methods of summation replace the ( C , 1 ) -method ordinarily used , are proved by Cohen [ 2 ] , Hille [ 1 ; Chap . 14 ] and Phillips [ 4 ] . Pointwise ergodic theorem . This theorem was ...
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