Linear Operators, Part 1 |
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Page 182
Thus da / dụ is defined u - almost everywhere by the formula ( da 2 ( E ) = u ( ds )
, Εε Σ . We close this section with a generalization of many " change of variable ”
theorems . 8 LEMMA . Let S , and S , be sets and $ a mapping of S , into Sz . If !
Thus da / dụ is defined u - almost everywhere by the formula ( da 2 ( E ) = u ( ds )
, Εε Σ . We close this section with a generalization of many " change of variable ”
theorems . 8 LEMMA . Let S , and S , be sets and $ a mapping of S , into Sz . If !
Page 240
It is evident that if we define the set function u on { by placing ( E ) = 0 if E $ and (
$ ) = 0 , then a bounded function is E ... The space B ( S ) is defined for an
arbitrary set S and consists of all bounded scalar functions on S. The norm is
given by ...
It is evident that if we define the set function u on { by placing ( E ) = 0 if E $ and (
$ ) = 0 , then a bounded function is E ... The space B ( S ) is defined for an
arbitrary set S and consists of all bounded scalar functions on S. The norm is
given by ...
Page 516
38 ( Markov ) Let S be a non - void set and $ a function on S to S. A function u
defined on the family of subsets of S is said to be 6 - invariant in case u ( E ) = u (
0-1E ) , ECS , where 6-1E = [ sos e E. Show that there is a non - negative
bounded ...
38 ( Markov ) Let S be a non - void set and $ a function on S to S. A function u
defined on the family of subsets of S is said to be 6 - invariant in case u ( E ) = u (
0-1E ) , ECS , where 6-1E = [ sos e E. Show that there is a non - negative
bounded ...
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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 |