## Linear Operators: General theory |

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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 ...

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### Contents

Metric Spaces | 19 |

Convergence and Uniform Convergence of Generalized | 26 |

Exercises | 33 |

Copyright | |

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