## Linear Operators: General theory |

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Page 95

Finitely Additive Set

process is

integral v ...

Finitely Additive Set

**Functions**In contrast to the terms real**function**, complex**function**, etc . , where the adjectives real and ... Thus , even if the integrationprocess is

**defined**with respect to a scalar valued set**function**u , the resultingintegral v ...

Page 98

The total variation of an additive set

S is also additive on E . PROOF . Let { A ; } be a finite sequence of disjoint sets in

with ACEUF where E , F € £ and EF = $ . Let E ; = EAi , Fi = FA , then Elu ( A ...

The total variation of an additive set

**function defined**on a field of subsets of a setS is also additive on E . PROOF . Let { A ; } be a finite sequence of disjoint sets in

with ACEUF where E , F € £ and EF = $ . Let E ; = EAi , Fi = FA , then Elu ( A ...

Page 182

Q . E . D . Note : The unique u - integrable

the Radon - Nikodım derivative of a with respect to u and is often denoted by da /

du . Thus da / du is

Q . E . D . Note : The unique u - integrable

**functions**of Theorems 2 and 7 is calledthe Radon - Nikodım derivative of a with respect to u and is often denoted by da /

du . Thus da / du is

**defined**u - almost everywhere by the formula 2 ( E ) = ( s ) ...### What people are saying - Write a review

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### Contents

Metric Spaces | 19 |

Convergence and Uniform Convergence of Generalized | 26 |

Exercises | 33 |

Copyright | |

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