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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 ... 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 ... non - negative extension to the o - field determined by E. If u is o - finite on then this extension is unique .
Page 202
We will first show that u is unique . Let , be another additive set function on £ , with the stated value on elementary sets . For each a let Mae do be set functions on E , defined by the formulas My ( En ) = u ( E , XS2 . ) ...
We will first show that u is unique . Let , be another additive set function on £ , with the stated value on elementary sets . For each a let Mae do be set functions on E , defined by the formulas My ( En ) = u ( E , XS2 . ) ...
Page 516
43 Show that in Exercise 39 the measure u is unique up to a positive constant factor if and only if n - 1 X = 01 ( $ ' ( s ) ) converges uniformly to a constant for each f € C ( S ) . 44 Let S be a compact metric space , and $ : S → S ...
43 Show that in Exercise 39 the measure u is unique up to a positive constant factor if and only if n - 1 X = 01 ( $ ' ( s ) ) converges uniformly to a constant for each f € C ( S ) . 44 Let S be a compact metric space , and $ : S → S ...
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Contents
Preliminary Concepts | 1 |
B Topological Preliminaries | 10 |
quences | 26 |
Copyright | |
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Akad algebra Amer analytic applied arbitrary assume B-space Banach Banach spaces bounded called clear closed compact complex Consequently contains continuous functions converges convex Corollary countably additive defined DEFINITION denote dense determined differential disjoint domain element equation equivalent everywhere Exercise exists extension field finite follows function defined function f given Hence implies inequality integral interval isomorphism Lebesgue Lemma limit linear functional linear operator linear space mapping Math mean measure space metric space neighborhood norm o-field open set operator positive problem Proc PROOF properties proved range regular respect Russian satisfies scalar seen separable sequence set function Show shown sphere statement subset Suppose Theorem theory topological space topology transformations u-integrable u-measurable uniformly union unique unit valued vector weak zero