## Linear Operators: General theory |

### From inside the book

Results 1-3 of 75

Page 100

It follows immediately from Lemma 10 that every subset of a u - null set , and

every finite union of u - null sets , is a u - null set . Any statement concerning the

points of S is said to hold u - almost

almost ...

It follows immediately from Lemma 10 that every subset of a u - null set , and

every finite union of u - null sets , is a u - null set . Any statement concerning the

points of S is said to hold u - almost

**everywhere**, or , if u is understood , simplyalmost ...

Page 150

13 COROLLARY . ( a ) If ( S , E , u ) is a measure space , a sequence of

measurable functions convergent in measure has a subsequence which

converges almost

almost

13 COROLLARY . ( a ) If ( S , E , u ) is a measure space , a sequence of

measurable functions convergent in measure has a subsequence which

converges almost

**everywhere**. ( b ) If ( S , E , u ) is a finite measure space , analmost

**everywhere**...Page 722

Show that if S is a topological space , and if , for each a > 0 , R ( 2 ; A ) is

continuous if f is continuous , then for 1 sp < oo and f e L , the limit lim , 70 ( 7R ( 2

; A ) f ) ( s ) exists almost

S1 ...

Show that if S is a topological space , and if , for each a > 0 , R ( 2 ; A ) is

continuous if f is continuous , then for 1 sp < oo and f e L , the limit lim , 70 ( 7R ( 2

; A ) f ) ( s ) exists almost

**everywhere**. 22 Let T be a transformation in Lj , T20 , TS1 ...

### What people are saying - Write a review

User Review - Flag as inappropriate

i want to read

### Contents

Metric Spaces | 19 |

Convergence and Uniform Convergence of Generalized | 26 |

Exercises | 33 |

Copyright | |

10 other sections not shown

### Other editions - View all

### Common terms and phrases

Acad algebra Amer analytic applied arbitrary assumed B-space Banach Banach spaces bounded called clear closed compact complex contains continuous functions converges convex Corollary countably additive defined DEFINITION denote dense determined differential disjoint Doklady Akad domain elements 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 operator positive problem Proc PROOF properties proved range regular respect Russian satisfies scalar seen semi-group 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