## 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 A ; CEUF where E , F e E and EF = 0 . Let E ; = EA , 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 A ; CEUF where E , F e E and EF = 0 . Let E ; = EA , Fi = FA , then Elu ( A ...

Page 182

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

Radon - Nikodým derivative of 2 with respect to u and is often denoted by da / du

. Thus da du is

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

**function**of Theorems 2 and 7 is called theRadon - Nikodým derivative of 2 with respect to u and is often denoted by da / du

. Thus da du is

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

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

Algebraic Preliminaries | 34 |

Copyright | |

80 other sections not shown

### Common terms and phrases

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