Linear Operators: General theory |
From inside the book
Results 1-3 of 95
Page 95
Finitely Additive Set Functions In contrast to the terms real function , complex
function , etc . , where the adjectives real ... of the function , the term set function is
commonly used in mathematics for a function whose domain is a family of sets .
Finitely Additive Set Functions In contrast to the terms real function , complex
function , etc . , where the adjectives real ... of the function , the term set function is
commonly used in mathematics for a function whose domain is a family of sets .
Page 96
Nelson Dunford, Jacob T. Schwartz. the med 96 III . INTEGRATION AND SET
FUNCTIONS III . 1 . 2 2 DEFINITION . A set function u defined on a family of sets
is said to be additive or finitely additive it u = ) and u ( A4U Ag . . . U An ) = u ( A1 )
+ ...
Nelson Dunford, Jacob T. Schwartz. the med 96 III . INTEGRATION AND SET
FUNCTIONS III . 1 . 2 2 DEFINITION . A set function u defined on a family of sets
is said to be additive or finitely additive it u = ) and u ( A4U Ag . . . U An ) = u ( A1 )
+ ...
Page 131
Let 2 , u be finitely additive set functions defined on a field E . Then 2 is said to be
continuous with respect to u or simply M - continuous , if lim 2 ( E ) = 0 . olu , E ) →
0 . The function 2 is said to be u - singular if there is a set E . c & such that v ( u ...
Let 2 , u be finitely additive set functions defined on a field E . Then 2 is said to be
continuous with respect to u or simply M - continuous , if lim 2 ( E ) = 0 . olu , E ) →
0 . The function 2 is said to be u - singular if there is a set E . c & such that v ( u ...
What people are saying - Write a review
We haven't found any reviews in the usual places.
Contents
Preliminary Concepts | 1 |
B Topological Preliminaries | 10 |
Algebraic Preliminaries | 34 |
Copyright | |
31 other sections not shown
Other editions - View all
Common terms and phrases
algebra Amer analytic applied arbitrary assumed B-space Banach spaces bounded called clear closed compact operator complex condition Consequently constant contains continuous functions converges convex convex set Corollary countably additive defined DEFINITION denote dense determined differential dimensional 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 neighborhood norm operator operator topology problem projection PROOF properties proved range reflexive representation respect satisfies scalar seen semi-group separable sequence set function Show shown statement subset subspace sufficient Suppose Theorem theory topology u-measurable uniform uniformly unique unit sphere valued vector weak weakly compact zero