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Page 81
Theorems 1.11 , 1.17 , and 1.18 were proved for linear functionals on a general B - space by Hahn [ 2 ] who applied ... Banach and Steinhaus [ 1 ; p , 53 ] observed that in the case of a Bspace Theorem 1.11 remains valid if { Taxa e A } ...
Theorems 1.11 , 1.17 , and 1.18 were proved for linear functionals on a general B - space by Hahn [ 2 ] who applied ... Banach and Steinhaus [ 1 ; p , 53 ] observed that in the case of a Bspace Theorem 1.11 remains valid if { Taxa e A } ...
Page 82
theorems or to give generalizations of some theorems of Saks [ 2 , 3 ] on sequences of measures . ... Orlicz [ 7 ] proves a theorem of the condensation type where the double sequence of operators also depends on a parameter in a ...
theorems or to give generalizations of some theorems of Saks [ 2 , 3 ] on sequences of measures . ... Orlicz [ 7 ] proves a theorem of the condensation type where the double sequence of operators also depends on a parameter in a ...
Page 729
Theorems for abstract vector lattices were proved by G. Birkhoff [ 2 ] , Kakutani [ 7 , 8 ] , and F. Riesz [ 17 ] . Several generalizations of the mean ergodic theorem to groups or semi - groups of operators more general than the ...
Theorems for abstract vector lattices were proved by G. Birkhoff [ 2 ] , Kakutani [ 7 , 8 ] , and F. Riesz [ 17 ] . Several generalizations of the mean ergodic theorem to groups or semi - groups of operators more general than the ...
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Contents
Preliminary Concepts | 1 |
B Topological Preliminaries | 10 |
quences | 26 |
Copyright | |
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Akad algebra Amer analytic applied arbitrary assume B-space Banach Banach spaces bounded called clear closed compact complex Consequently contains continuous functions converges convex Corollary countably additive defined DEFINITION denote dense determined differential disjoint domain element equation equivalent everywhere Exercise exists extension field finite follows function defined function f given Hence implies inequality integral interval isomorphism Lebesgue Lemma limit linear functional linear operator linear space mapping Math mean measure space metric space neighborhood norm o-field open set operator positive problem Proc PROOF properties proved range regular respect Russian satisfies scalar seen separable sequence set function Show shown sphere statement subset Suppose Theorem theory topological space topology transformations u-integrable u-measurable uniformly union unique unit valued vector weak zero