Linear Operators, Part 1 |
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Page 136
There is a uniquely determined smallest field and a uniquely determined smallest
o - field containing a given family of sets . Proof . There is at least one field ,
namely the field of all subsets of S , which contains a given family t . The
intersection ...
There is a uniquely determined smallest field and a uniquely determined smallest
o - field containing a given family of sets . Proof . There is at least one field ,
namely the field of all subsets of S , which contains a given family t . The
intersection ...
Page 166
If we put E ( E ) = { F € E F C E } it is clear that E ( E ) is a field of subsets of E , and
that E ( E ) is the family of all sets AE , A € X , and that if Eis a o - field , then E ( E )
is a o - field . Σ ( Ε ) is called the restriction of Σ to E. If Σ , is a field , Εε Σ . , and ...
If we put E ( E ) = { F € E F C E } it is clear that E ( E ) is a field of subsets of E , and
that E ( E ) is the family of all sets AE , A € X , and that if Eis a o - field , then E ( E )
is a o - field . Σ ( Ε ) is called the restriction of Σ to E. If Σ , is a field , Εε Σ . , and ...
Page 201
The symbol will be used for the o - field of sets in S determined by Ey . The family
of all sets in S of the form S , XER with Ε ε Σ will be denoted by Σπ . 18 LEMMA .
For each a the family In is a field of sets in S and Ei = U241 . PROOF .
The symbol will be used for the o - field of sets in S determined by Ey . The family
of all sets in S of the form S , XER with Ε ε Σ will be denoted by Σπ . 18 LEMMA .
For each a the family In is a field of sets in S and Ei = U241 . PROOF .
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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, Nelson Dunford Volume 1 of Linear Operators: General Theory. Spectral Theory, Self Adjoint Operators in Hilbert Space. Spectral Operators. I. II. III, Jacob T. Schwartz Volume 7 of Pure & Applied Mathematics : a Wiley-interscience series of texts, monographs & tracts Volume 7 of Pure and applied mathematics : a series of texts and monographs Pure and applied mathematics, ISSN 0079-8185 Wiley classics library |
| Authors | Nelson Dunford, Jacob T. Schwartz, William G. Bade, Robert G. Bartle |
| Editors | William G. Bade, Robert G. Bartle |
| Edition | reprint |
| Publisher | Interscience Publishers, 1958 |
| Original from | the University of California |
| Digitized | 26 Jun 2018 |
| ISBN | 0470226056, 9780470226056 |
| Length | 2592 pages |
| Export Citation | BiBTeX EndNote RefMan |