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Page 100
It follows immediately from Lemma 10 that every subset of a u - null set , and
every finite union of u - null sets , is a u - null set . Any statement concerning the
points of S is said to hold u - almost everywhere , or , if u is understood , simply
almost ...
It follows immediately from Lemma 10 that every subset of a u - null set , and
every finite union of u - null sets , is a u - null set . Any statement concerning the
points of S is said to hold u - almost everywhere , or , if u is understood , simply
almost ...
Page 150
13 COROLLARY . ( a ) If ( S , E , u ) is a measure space , a sequence of
measurable functions convergent in measure has a subsequence which
converges almost everywhere . ( b ) If ( S , E , u ) is a finite measure space , an
almost everywhere ...
13 COROLLARY . ( a ) If ( S , E , u ) is a measure space , a sequence of
measurable functions convergent in measure has a subsequence which
converges almost everywhere . ( b ) If ( S , E , u ) is a finite measure space , an
almost everywhere ...
Page 722
Show that if S is a topological space , and if , for each a > 0 , R ( 2 ; A ) is
continuous if f is continuous , then for 1 sp < oo and f e L , the limit lim , 70 ( 7R ( 2
; A ) f ) ( s ) exists almost everywhere . 22 Let T be a transformation in Lj , T20 , T
S1 ...
Show that if S is a topological space , and if , for each a > 0 , R ( 2 ; A ) is
continuous if f is continuous , then for 1 sp < oo and f e L , the limit lim , 70 ( 7R ( 2
; A ) f ) ( s ) exists almost everywhere . 22 Let T be a transformation in Lj , T20 , T
S1 ...
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Contents
Metric Spaces | 19 |
Convergence and Uniform Convergence of Generalized | 26 |
Exercises | 33 |
Copyright | |
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Acad algebra Amer analytic applied arbitrary assumed B-space Banach Banach spaces bounded called clear closed compact complex contains continuous functions converges convex Corollary countably additive defined DEFINITION denote dense determined differential disjoint Doklady Akad domain elements equation equivalent everywhere Exercise exists extension field finite follows function defined function f given Hence Hilbert space implies inequality integral interval isomorphism Lebesgue Lemma limit linear functional linear operator linear space mapping Math mean measure space metric space neighborhood norm operator positive problem Proc PROOF properties proved range regular respect Russian satisfies scalar seen semi-group 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
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Bibliographic information
| Title | Linear Operators: General theory Part 1 of Linear Operators, Jacob T. Schwartz Volume 1; Volume 7 of Pure and applied mathematics : a series of texts and monographs Volume 7 of Pure and applied mathematics Interscience Press Pure and applied mathematics, ISSN 0079-8185 Wiley classics library |
| Authors | Nelson Dunford, Jacob T. Schwartz, William G. Bade |
| Publisher | Interscience Publishers, 1958 |
| Original from | the University of Michigan |
| Digitized | 20 Nov 2007 |
| ISBN | 0470226056, 9780470226056 |
| Length | 2592 pages |
| Export Citation | BiBTeX EndNote RefMan |