## Linear Operators: General theory |

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Page 95

Finitely Additive

function , etc . , where the adjectives real ... of the function , the term

commonly used in mathematics for a function whose domain is a family of sets .

Finitely Additive

**Set Functions**In contrast to the terms real function , complexfunction , etc . , where the adjectives real ... of the function , the term

**set function**iscommonly used in mathematics for a function whose domain is a family of sets .

Page 96

A

additive if u ( d ) = 0 and u ( A , U AZ . . . U An ) = u ( A2 ) + ( A2 ) + . . . + u ( An ) ,

for every finite family { Aj , . . . , An } of disjoint subsets of T whose union is in t .

For an ...

A

**set function**u defined on a family T of sets : 3 said to be additive or finitelyadditive if u ( d ) = 0 and u ( A , U AZ . . . U An ) = u ( A2 ) + ( A2 ) + . . . + u ( An ) ,

for every finite family { Aj , . . . , An } of disjoint subsets of T whose union is in t .

For an ...

Page 184

We shall denote by E the family of all sets in the Cartesian product S = S , X . . .

XSn of the form E = E , X . . . x En , where E ; € £i 1 LEMMA . For i = 1 , . . . , n , let

u ; be a finitely additive complex valued

We shall denote by E the family of all sets in the Cartesian product S = S , X . . .

XSn of the form E = E , X . . . x En , where E ; € £i 1 LEMMA . For i = 1 , . . . , n , let

u ; be a finitely additive complex valued

**set function**defined on a field £ ; of ...### What people are saying - Write a review

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### Contents

Special Spaces | 237 |

Convex Sets and Weak Topologies | 409 |

General Spectral Theory | 555 |

Copyright | |

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