## Linear Operators: General theory |

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Page 112

A function f on S to X is

A function f on S to X is

**u**-**integrable**on S if there is a sequence { { n } of**u**-**integrable**simple functions converging to f in j - measure on S and ...Page 113

18 LEMMA . A function f on S is

18 LEMMA . A function f on S is

**u**-**integrable**if and only if it is v (**u**) -**integrable**. If f is j -**integrable**so is \ ( ( . ) ) .Page 180

Sleds ) = f ( s ) g ( s )

Sleds ) = f ( s ) g ( s )

**u**( ds ) . Εε Σ . PROOF . Suppose that g is 2 -**integrable**. By Lemma 3 , fg is measurable . The**u**-**integrability**of tg follows ...### What people are saying - Write a review

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

quences | 26 |

Copyright | |

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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