## Linear Operators, Part 1 |

### From inside the book

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Page 106

The functions 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 off with the

characteristic ...

The functions totally

**u**-**measurable**on S , or , if u is understood , totallymeasurable 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 off with the

characteristic ...

Page 149

If ( S , E , u ) is a measure space , then a function | on S to a B - space X is

function | is u - essentially separably valued on F , and ( ii ) for every linear

functional x ...

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 , thefunction | is u - essentially separably valued on F , and ( ii ) for every linear

functional x ...

Page 178

XF ( s ) / ( s ) g ( s ) = lim % F , ( s ) / ( s ) g ( s ) , SES , and the pointwise limit of a

sequence of

% 5,1g is

XF ( s ) / ( s ) g ( s ) = lim % F , ( s ) / ( s ) g ( s ) , SES , and the pointwise limit of a

sequence of

**measurable**functions is**measurable**, it will suffice then to show that% 5,1g is

**measurable**. Thus we may and shall assume that v (**u**, F ) < oo and v ...### 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

### Common terms and phrases

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