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Page 387
A detailed proof was given by Fréchet [ 5 ; III . p . 441 ] . The theorem for L [ 0 , 1 ] ,
1 < p < 0o , was demonstrated by F . Riesz [ 2 ; p . 475 ] . In the case of a finite
measure space the theorem was established by Nikodým [ 9 ; p . 132 ] and later
by ...
A detailed proof was given by Fréchet [ 5 ; III . p . 441 ] . The theorem for L [ 0 , 1 ] ,
1 < p < 0o , was demonstrated by F . Riesz [ 2 ; p . 475 ] . In the case of a finite
measure space the theorem was established by Nikodým [ 9 ; p . 132 ] and later
by ...
Page 392
tion with respect to a vector valued measure which is presented here is the one
given in Bartle , Dunford and Schwartz [ 1 ] . A similar procedure has been
employed by Bartle [ 3 ] to obtain a Lebesgue - type integration theory where both
...
tion with respect to a vector valued measure which is presented here is the one
given in Bartle , Dunford and Schwartz [ 1 ] . A similar procedure has been
employed by Bartle [ 3 ] to obtain a Lebesgue - type integration theory where both
...
Page 729
proofs , valid in uniformly convex spaces , were given by G . Birkhoff [ 7 ] and F .
Riesz [ 16 , 18 ] . Another proof , based on the interesting fact that a fixed point for
a contraction in Hilbert space is also a fixed point for its adjoint , was given by ...
proofs , valid in uniformly convex spaces , were given by G . Birkhoff [ 7 ] and F .
Riesz [ 16 , 18 ] . Another proof , based on the interesting fact that a fixed point for
a contraction in Hilbert space is also a fixed point for its adjoint , was given by ...
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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 |