## Linear Operators: General theory |

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Page 95

In some cases that will be encountered the values of u are not scalars , but customarily where integration is used in this text u is a scalar

In some cases that will be encountered the values of u are not scalars , but customarily where integration is used in this text u is a scalar

**valued**function and f a vector ( or scalar )**valued**function . Thus , even if the integration ...Page 318

Vector

Vector

**Valued**Measures The theorems on spaces of set functions proved in the last section permit us to develop a more satisfactory theory of vector**valued**countably additive set functions ( briefly , vector**valued**measures ) than we ...Page 323

A scalar

A scalar

**valued**measurable function f is said to be integrable if there exists a sequence { { n } of simple functions such that ( i ) fn ( s ) converges to f ( s ) u - almost everywhere ; ( ii ) the sequence { Sein ( s ) ...### 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