## Linear Operators: General theory |

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Page 98

The total variation of an additive set

The total variation of an additive set

**function defined**on a field of subsets of a set S is also additive on E. PROOF . Let { A ; } be a finite sequence of ...Page 101

In these sections f will be a vector valued

In these sections f will be a vector valued

**function defined**on a set S and u a finitely additive set**function defined**on a field of subsets of S. It will ...Page 182

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

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

**function**of Theorems 2 and 7 is called the ... mz ( d.sy ) ; ( f ) if a**function**f**defined**on S , is uy - integrable ...### What people are saying - Write a review

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

quences | 26 |

Copyright | |

80 other sections not shown

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### Common terms and phrases

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