Linear Operators: General theory |
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Page 195
with respect to one variable and then with respect to the other , or vice versa . Indeed , according to Tonelli's theorem , both these integrals are equal to the integral off with respect to the product measure ( and we have already ...
with respect to one variable and then with respect to the other , or vice versa . Indeed , according to Tonelli's theorem , both these integrals are equal to the integral off with respect to the product measure ( and we have already ...
Page 306
The functions ilon are all continuous with respect to the measure defined by 1 v ( Mn , E ) 2 ( E ) Εε Σ , , n = 12 " 1 + v ( um , E ) ' and thus all belong to the subspace ca ( S , E , a ) consisting of all 2 - continuous functions in ...
The functions ilon are all continuous with respect to the measure defined by 1 v ( Mn , E ) 2 ( E ) Εε Σ , , n = 12 " 1 + v ( um , E ) ' and thus all belong to the subspace ca ( S , E , a ) consisting of all 2 - continuous functions in ...
Page 341
( ii ) There is a non - negative u in ba ( S , 2 ) with respect to which every à in K is continuous . ( iii ) lim , U = uniformly with respect to a € K. 20 Let & { En } be a countable field of subsets of a set S , and let & be the o ...
( ii ) There is a non - negative u in ba ( S , 2 ) with respect to which every à in K is continuous . ( iii ) lim , U = uniformly with respect to a € K. 20 Let & { En } be a countable field of subsets of a set S , and let & be the o ...
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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