## Linear Operators: General theory |

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Page 136

There is a

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

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

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 ...### What people are saying - Write a review

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

quences | 26 |

Copyright | |

80 other sections not shown

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### Common terms and phrases

Akad algebra Amer analytic applied arbitrary assume B-space Banach Banach spaces bounded called clear closed compact complex Consequently contains 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 Hilbert space 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