## Linear Operators: General theory |

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Page 164

The field & is a subfield of E , and Mi the

The field & is a subfield of E , and Mi the

**restriction**of u from E to El . There are a number of elementary but useful relations between u- and yq - measurability , u- and yy - integrability , etc. , which will be discussed in the ...Page 166

Since \ / ( ) p converges to 11 ( • ) | ” in ply - measure , it follows from Definition 2.17 that \ ( ( :) | p is uy - integrable and thus that f € L ( u ) . Q.E.D. In addition to the

Since \ / ( ) p converges to 11 ( • ) | ” in ply - measure , it follows from Definition 2.17 that \ ( ( :) | p is uy - integrable and thus that f € L ( u ) . Q.E.D. In addition to the

**restriction**of u to a subfield of Ethere ...Page 168

Then there is a set s , in E , a sub o - field & of E ( S ) , and a closed separable subspace X of X such that the

Then there is a set s , in E , a sub o - field & of E ( S ) , and a closed separable subspace X of X such that the

**restriction**My of u to ; has the following properties : ( i ) the measure space ( S1 , E1 , M2 ) is o - finite ...### 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