Linear Operators, Part 1 |
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Page 100
Any statement concerning the points of S is said to hold u - almost everywhere ,
or , if u is understood , simply almost everywhere , or for almost all s in S , if it is
true except for those points s in a u - null set . The phrase " almost everywhere ...
Any statement concerning the points of S is said to hold u - almost everywhere ,
or , if u is understood , simply almost everywhere , or for almost all s in S , if it is
true except for those points s in a u - null set . The phrase " almost everywhere ...
Page 151
( Lebesgue dominated convergence theorem ) Let 1 sp < oo , let ( S , E , u ) be a
measure space , and let { fn } be a sequence of functions in L ( S , E , „ , X )
converging almost everywhere to a function f . Suppose that there exists a
function g in ...
( Lebesgue dominated convergence theorem ) Let 1 sp < oo , let ( S , E , u ) be a
measure space , and let { fn } be a sequence of functions in L ( S , E , „ , X )
converging almost everywhere to a function f . Suppose that there exists a
function g in ...
Page 676
For such a vector h we have A ( T , n ) h = f + ( I – T " ) g / n , and thus , for almost
all s in S , we have | AT , n ) ( h , s ) - | ( s ) = 2glon → 0 . This shows that AT , nbh
converges almost everywhere for every h in a dense set in L , and , by Lemma 5 ...
For such a vector h we have A ( T , n ) h = f + ( I – T " ) g / n , and thus , for almost
all s in S , we have | AT , n ) ( h , s ) - | ( s ) = 2glon → 0 . This shows that AT , nbh
converges almost everywhere for every h in a dense set in L , and , by Lemma 5 ...
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Contents
Preliminary Concepts | 1 |
The VitaliHahnSaks Theorem and Spaces of Measures | 7 |
B Topological Preliminaries | 10 |
Copyright | |
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Akad algebra Amer analytic applied arbitrary assumed B-space Banach Banach spaces bounded called clear closed complex Consequently contains converges convex Corollary defined DEFINITION denote dense determined differential dimensional disjoint domain element equation equivalent everywhere Exercise exists extension field finite follows function defined function f given Hence Hilbert space identity implies inequality integral interval isomorphism Lebesgue Lemma limit linear functional linear operator linear space Math measure space metric space neighborhood norm open set positive measure problem projection Proof properties proved range reflexive representation respect Russian satisfies scalar seen separable sequence set function Show shown sphere statement subset Suppose Theorem theory topological space topology u-measurable uniform uniformly unique unit valued vector weak weakly compact zero
Bibliographic information
| Title | Linear Operators, Part 1 Linear Operators, Jacob T. Schwartz Volume 7 of Mathematics, Pure, Applied Volume 7 of Pure and applied mathematics, ISSN 0079-8185 Volume 7 of Pure and applied mathematics. A series of texts and monographs |
| Authors | Nelson Dunford, Jacob T. Schwartz |
| Publisher | Interscience Publishers, 1958 |
| Original from | the University of California |
| Digitized | 26 Jun 2018 |
| Length | 2592 pages |
| Export Citation | BiBTeX EndNote RefMan |