## Linear Operators: General theory |

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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 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

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

sequence of

Xe fg is

...

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

sequence of

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

**measurable**. Thus we may and shall assume that v (**u**, F ) < oo and v ( 2...

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### Contents

Metric Spaces | 19 |

Convergence and Uniform Convergence of Generalized | 26 |

Exercises | 33 |

Copyright | |

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