## Linear Operators: General theory |

### From inside the book

Results 1-3 of 93

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 satisfying in addition the equation lim ss \ 1m ( s ) –In ( s ) [ 0 \**u**, ds ) = 0 .Page 113

A function f on S is

A function f on S is

**u**-**integrable**if and only if it is v (**u**) -**integrable**. If f is j -**integrable**so is \ ( ( . ) ) . If { { n } is a sequence of -**integrable**simple functions determining f in accordance with the preceding ...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 from Theorem 2.22 when it is observed ( by Theorem 4 ) that \ | ( • ) g ( ) is**u**...### What people are saying - Write a review

We haven't found any reviews in the usual places.

### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

quences | 26 |

Copyright | |

80 other sections not shown

### Other editions - View all

### 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