## Linear Operators, Part 1 |

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Page 136

There is a

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

There is a

**uniquely**determined smallest field and a**uniquely**determined smallesto - 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

We will first show that u is

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 ) = 2 ( EnXS ,, ) , E ...

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 ) = 2 ( EnXS ,, ) , E ...

Page 516

42 Show that in Exercise 38 the set function u is

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

42 Show that in Exercise 38 the set function u is

**unique**up to a positive constantfactor 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 ...### 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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