## Linear Operators: General theory |

### From inside the book

Results 1-3 of 84

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 xet 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 xet off with the

characteristic ...

Page 119

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

is

extended real - valued ) which is defined only on the complement of a u - null set

NCS .

( b ) the function g defined by g ( s ) = 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 orextended real - valued ) which is defined only on the complement of a u - null set

NCS .

Page 178

ZF ( 8 ) / ( 8 ) g ( 8 ) = lim % , ( ) / ( s ) g ( s ) , SES , and the pointwise limit of a

sequence of

me fg is

F ) ...

ZF ( 8 ) / ( 8 ) g ( 8 ) = lim % , ( ) / ( s ) g ( s ) , SES , and the pointwise limit of a

sequence of

**measurable**functions is**measurable**, it will suffice then to show thatme fg is

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

### What people are saying - Write a review

User Review - Flag as inappropriate

i want to read

### Contents

Special Spaces | 237 |

Convex Sets and Weak Topologies | 409 |

General Spectral Theory | 555 |

Copyright | |

5 other sections not shown

### Other editions - View all

### Common terms and phrases

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