## Linear Operators: General theory |

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Page 95

Finitely Additive

Finitely Additive

**Set Functions**In contrast to the terms real function , complex function , etc. , where the adjectives real and complex refer to the range of the function , the term**set function**is commonly used in mathematics for a ...Page 96

A

A

**set function**u defined on a family t of sets is said to be additive or finitely additive if u ( t ) = 0 and u ( A U AZ ... U An ) = u ( A1 ) + u ( A2 ) + ... + u ( An ) , for every finite family { A , ... , An } of disjoint subsets of ...Page 837

A on Abel summability , of series , II.4.42 ( 76 ) Abelian group , ( 34 ) Absolutely continuous functions , definition , IV.2.22 ( 242 )

A on Abel summability , of series , II.4.42 ( 76 ) Abelian group , ( 34 ) Absolutely continuous functions , definition , IV.2.22 ( 242 )

**set function**. ( See Continuous**set function**and**Set function**) space of , additional properties ...### What people are saying - Write a review

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

Algebraic Preliminaries | 34 |

Copyright | |

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### Common terms and phrases

algebra Amer analytic applied arbitrary assumed B-space Banach Banach spaces bounded called clear closed compact complex condition Consequently contains continuous functions converges convex Corollary countably additive defined DEFINITION denote dense determined differential disjoint element equation equivalent everywhere Exercise exists extension field finite follows function defined function f given Hence Hilbert space implies inequality integral interval isometric isomorphism Lebesgue Lemma limit linear functional linear operator linear space mapping Math meaning measure space metric neighborhood norm obtained operator positive measure problem Proc PROOF properties proved regular respect Russian satisfies scalar seen semi-group separable sequence set function Show shown sphere statement subset sufficient Suppose Theorem theory topology u-measurable uniform uniformly unique unit valued vector weak weakly compact zero