## Linear Operators: General theory |

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Page 182

Thus da / du is

) , Ee E . We close this section with a generalization of many “ change of variable

” theorems . 8 LEMMA . Let S , and S , be sets and $ a mapping of S , into Sz . If ...

Thus da / du is

**defined**u - almost everywhere by the formula 2 ( E ) = ( s ) qu ( ds) , Ee E . We close this section with a generalization of many “ change of variable

” theorems . 8 LEMMA . Let S , and S , be sets and $ a mapping of S , into Sz . If ...

Page 240

It is evident that if we

and uld ) ... The space B ( S ) is

bounded scalar functions on S . The norm is given by W = sup \ | ( s ) . SES 14 .

It is evident that if we

**define**the set function u on { by placing u ( E ) = 0 if E + $and uld ) ... The space B ( S ) is

**defined**for an arbitrary set S and consists of allbounded scalar functions on S . The norm is given by W = sup \ | ( s ) . SES 14 .

Page 241

u , S ) . 18 . The space L ( S , E , u ) is

and any positive measure space ( S , E , ) . It consists of those u - measurable ...

**defined**on the o - field B of all Borel sets in S . The norm ul is the total variation v (u , S ) . 18 . The space L ( S , E , u ) is

**defined**for any real number p , 13p < 0 ,and any positive measure space ( S , E , ) . It consists of those u - measurable ...

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### Contents

Metric Spaces | 19 |

Convergence and Uniform Convergence of Generalized | 26 |

Exercises | 33 |

Copyright | |

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