Linear Operators: General theory |
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Page 100
Let u be an additive set function defined on a field of subsets of a set S . A subset
N of S is said to be a u - null set if v * ( u , N ) ... 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
...
Let u be an additive set function defined on a field of subsets of a set S . A subset
N of S is said to be a u - null set if v * ( u , N ) ... 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
...
Page 147
A set is a null set if and only if it is a subset of some measurable set F such that v (
u , F ) = 0 . PROOF . If E is a null set , then v * ( u , E ) = 0 and there are
measurable sets En containing E with v ( u , En ) < 1 / n . Thus the set F = n E , is
a ...
A set is a null set if and only if it is a subset of some measurable set F such that v (
u , F ) = 0 . PROOF . If E is a null set , then v * ( u , E ) = 0 and there are
measurable sets En containing E with v ( u , En ) < 1 / n . Thus the set F = n E , is
a ...
Page 213
( a ) If for each p in a set ACG 2 ( C ) lim inf . < ? ' , H ( C ) - 0 u ( C ) where C is a
closed cube containing p , then each neighborhood of A contains an open set Q
such that A - Q is a d - null set and 1 ( Q ) < ru ( Q ) . ( b ) If for each p in a set A CG
...
( a ) If for each p in a set ACG 2 ( C ) lim inf . < ? ' , H ( C ) - 0 u ( C ) where C is a
closed cube containing p , then each neighborhood of A contains an open set Q
such that A - Q is a d - null set and 1 ( Q ) < ru ( Q ) . ( b ) If for each p in a set A CG
...
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Contents
Preliminary Concepts | 1 |
B Topological Preliminaries | 10 |
Algebraic Preliminaries | 34 |
Copyright | |
21 other sections not shown
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Linear Operators, Part 1 Nelson Dunford,Jacob T. Schwartz,William G. Bade,Robert G. Bartle Snippet view - 1958 |
Common terms and phrases
algebra Amer analytic applied arbitrary assumed B-space Banach Banach spaces bounded called clear closed compact complex Consequently constant contains converges convex Corollary defined DEFINITION denote dense determined differential disjoint domain element equation equivalent everywhere Exercise exists extension field finite follows formula function defined function f given Hence Hilbert space identity implies inequality integral interval Lebesgue Lemma limit linear functional linear operator linear space Math mean measure space metric neighborhood norm positive measure problem Proc projection PROOF properties proved respect Russian satisfies scalar seen semi-group separable sequence set function Show shown sphere statement strongly subset sufficient Suppose Theorem theory topological space topology transformations u-measurable uniform uniformly unique unit valued vector weak weakly compact zero
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 |
| Authors | Nelson Dunford, Jacob T. Schwartz |
| Publisher | Interscience Publishers, 1958 |
| Length | 2592 pages |
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