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 . ... additive non - negative extension to
the o - field determined by E. If u is o - finite on { then this extension is unique .
There is a uniquely determined smallest field and a uniquely determined smallest
o - field containing a given family of sets . ... additive non - negative extension to
the o - field determined by E. If u is o - finite on { then this extension is unique .
Page 202
Nelson Dunford, Jacob T. Schwartz. u ( P Ex ) = II Ma ( EQ ) , AEA αεΑ for every
elementary set Paca E , in S. Proof . We will first show that u is unique . Let 2 be
another additive set function on E , with the stated value on elementary sets .
Nelson Dunford, Jacob T. Schwartz. u ( P Ex ) = II Ma ( EQ ) , AEA αεΑ for every
elementary set Paca E , in S. Proof . We will first show that u is unique . Let 2 be
another additive set function on E , with the stated value on elementary sets .
Page 516
42 Show that in Exercise 38 the set function u is unique up to a positive constant
factor if and only if n - 1 X = d / ( $ ' ( s ) ) converges uniformly to a constant for
each je B ( S ) . 43 Show that in Exercise 39 the measure u is unique up to a ...
42 Show that in Exercise 38 the set function u is unique up to a positive constant
factor if and only if n - 1 X = d / ( $ ' ( s ) ) converges uniformly to a constant for
each je B ( S ) . 43 Show that in Exercise 39 the measure u is unique up to a ...
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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