## Linear Operators: General theory |

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Page 106

The functions totally

The functions totally

**u**-**measurable**on S , or , if**u**is understood , totally**measurable**on S are the functions in the closure TM ( S ) in F ( S ) of the**u**- simple functions . If for every E in with v (**u**, E ) < 00 , the product det ...Page 149

If ( S , E ,

If ( S , E ,

**u**) is a measure space , then a function | on S to a B - space X is**u**-**measurable**if and only if ( i ) for every**measurable**set F with v (**u**, F ) < 0 , the function | is**u**- essentially separably valued on F , and ( ii ) ...Page 178

Thus we may and shall assume that v (

Thus we may and shall assume that v (

**u**, F ) < oo and v ( a , F ) < 0 . Since g is a -**measurable**there is a sequence { gn } of simple functions converging to g ( s ) for every s in F except on a set E C F with v ( 2 , E ) = 0 ( by ...### 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 | |

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### Common terms and phrases

Akad algebra Amer analytic applied arbitrary assumed B-space Banach Banach spaces bounded called clear closed closure complex condition Consequently contains continuous functions converges Corollary defined DEFINITION denote dense determined differential disjoint element equation equivalent everywhere Exercise exists extension field finite follows formula function f given Hence Hilbert space implies integral interval isomorphism Lebesgue Lemma limit linear functional linear operator linear space linear topological space Math means measure space metric space neighborhood norm open set operator problem Proc projection Proof properties proved range reflexive respect Russian satisfies scalar seen semi-group separable sequence set function Show shown statement subset subspace sufficient Suppose Theorem theory topology u-measurable uniform uniformly unique unit sphere valued vector weak weakly compact zero