## 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

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

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 beanother 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

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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