## 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 ) < 0 , the product met ...Page 119

( b ) the function g defined by g ( 8 ) = f ( s ) if s & S + US- , g ( s ) = 0 if se S + US- , is

( b ) the function g defined by g ( 8 ) = f ( s ) if s & S + US- , g ( s ) = 0 if se S + US- , is

**u**-**measurable**. Next suppose that we consider a function f ( vector or extended real - valued ) which is defined only on the complement ...Page 178

Thus we may and shall assume that v (

Thus we may and shall assume that v (

**u**, F ) < oo and v ( 2 , F ) < oo . Since g is a -**measurable**there is a sequence { en } of simple functions converging to g ( s ) for every s in F except on a set ECF with v ( 2 , E ) = 0 ( by ...### What people are saying - Write a review

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### Contents

B Topological Preliminaries | 10 |

quences | 26 |

Algebraic Preliminaries | 34 |

Copyright | |

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Acad algebra Amer analytic applied arbitrary assumed B-space Banach Banach spaces bounded called clear closed compact complex condition contains continuous functions converges convex Corollary countably additive defined DEFINITION denote dense determined differential disjoint Doklady Akad 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 meaning measure space metric neighborhood norm operator positive measure problem Proc PROOF properties proved respect Russian satisfies scalar seen semi-group separable sequence set function Show shown sphere statement subset sufficient Suppose Theorem theory topological space topology transformations u-measurable uniform uniformly unique unit valued vector weak weakly compact zero