## Linear Operators, Part 1 |

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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 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

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

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