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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 |
10 | 30 |
Three Basic Principles of Linear Analysis | 49 |
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A₁ additive set function algebra analytic arbitrary B-space B₁ ba(S Banach Borel sets ca(S Cauchy sequence closed unit sphere compact Hausdorff space compact operator complex numbers conditionally compact contains continuous functions convex set Corollary countably additive DEFINITION denote dense E₁ element equation equivalent exists f₁ finite dimensional function defined function f Hausdorff space Hence Hilbert space homeomorphism implies inequality integral isometric isomorphism K₁ L₁ L₁(S Lebesgue measure Lemma Let f linear map linear operator linear topological space Math measurable functions measure space metric space neighborhood non-negative non-zero normed linear space o-field o-finite open set operator topology positive measure space properties proved real numbers reflexive Riesz S₁ scalar semi-group sequentially compact Show subset subspace Suppose theory TM(S topological space u-integrable u-measurable uniformly valued function weak topology weakly compact weakly sequentially compact X₁ zero ΕΕΣ