## Linear Operators: General theory |

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that is , for every a e A , the

g : B →C , then the mapping gf : A → C is defined by the equation ( gf ) ( a ) = g ( /

( a ) ) for a € A . If f : A → B and CCA , the symbol | ( C ) is used for the set of all ...

that is , for every a e A , the

**function f**assigns an element f ( a ) e B . If f : A + B andg : B →C , then the mapping gf : A → C is defined by the equation ( gf ) ( a ) = g ( /

( a ) ) for a € A . If f : A → B and CCA , the symbol | ( C ) is used for the set of all ...

Page 103

space of all functions which map S into X ( see 1 . 6 . 1 ) . Unfortunately , this is

rarely the case and so a slight detour will be made . 3 DEFINITION . The

on S to X is said to be a u - null function or , when u is understood , simply a null ...

space of all functions which map S into X ( see 1 . 6 . 1 ) . Unfortunately , this is

rarely the case and so a slight detour will be made . 3 DEFINITION . The

**function f**on S to X is said to be a u - null function or , when u is understood , simply a null ...

Page 196

Suppose that ( S , E , u ) is a measure space and

whose values are in L ( T , ET , 2 ) , 1 Sp < . 0 . For each s in S ,

equivalence class

Suppose that ( S , E , u ) is a measure space and

**F**is a u - measurable**function**whose values are in L ( T , ET , 2 ) , 1 Sp < . 0 . For each s in S ,

**F**( s ) is anequivalence class

**of functions**, any pair**of**whose members coincide h - almost ...### What people are saying - Write a review

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### Contents

Metric Spaces | 19 |

Convergence and Uniform Convergence of Generalized | 26 |

Exercises | 33 |

Copyright | |

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