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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
A Settheoretic Preliminaries | 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 Cauchy sequence compact operator complex numbers contains continuous functions continuous linear converges convex set Corollary countably additive DEFINITION denote dense differential equations disjoint Doklady Akad domain E₁ element exists f₁ finite dimensional finite number function defined function f Hausdorff space Hence Hilbert space homeomorphism inequality integral L₁ L₁(S Lebesgue Lemma Let f linear functional linear map linear operator linear topological space measurable function measure space metric space Nauk SSSR N. S. neighborhood non-negative o-field open set operator topology positive measure space Proc PROOF proved real numbers Riesz Russian S₁ scalar semi-group sequentially compact Show spectral strong operator topology subset subspace Suppose T₁ theory topological space u-integrable u-measurable uniformly unit sphere valued function weakly compact zero ΕΕΣ