## 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 ... 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 2 be another additive set function on E , with the stated value on elementary sets . For each r let uz , ha be set functions on En defined by the formulas Mz ( EZ ) = u ( EXS ,, ) , 27 ( Ez ) ...Page 516

42 Show that in Exercise 38 the set function u is

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

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### Contents

Preliminary Concepts | 1 |

The VitaliHahnSaks Theorem and Spaces of Measures | 7 |

B Topological Preliminaries | 10 |

Copyright | |

87 other sections not shown

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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