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Page 48
The first occurrence of a maximum principle equivalent to the well - ordering
principle ( as in Theorem 2 . 6 ) is in Hausdorff ( 1 ; p . 140 ] . Zorn [ 1 ] gave a
theorem essentially equivalent to Theorem 2 . 7 . A similar theorem is due to R . L
...
The first occurrence of a maximum principle equivalent to the well - ordering
principle ( as in Theorem 2 . 6 ) is in Hausdorff ( 1 ; p . 140 ] . Zorn [ 1 ] gave a
theorem essentially equivalent to Theorem 2 . 7 . A similar theorem is due to R . L
...
Page 91
admits an equivalent metric under which it is complete , then G admits an
invariant metric and is complete under each invariant metric . Thus every
complete linear metric space can be metrized to be an F - space . Further , a
normed linear ...
admits an equivalent metric under which it is complete , then G admits an
invariant metric and is complete under each invariant metric . Thus every
complete linear metric space can be metrized to be an F - space . Further , a
normed linear ...
Page 347
( b ) Show that L ( S , E , u ) is equivalent to l , if and only if there exists a
countable collection of atoms of finite measure { En } in such that every
measurable subset of S - UC _ En is either an atom of infinite measure or a null
set . 50 Show that ...
( b ) Show that L ( S , E , u ) is equivalent to l , if and only if there exists a
countable collection of atoms of finite measure { En } in such that every
measurable subset of S - UC _ En is either an atom of infinite measure or a null
set . 50 Show that ...
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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 |