## Linear Operators: General theory |

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Page 336

This implies that fı and f2 are

) and ( ( A ( { 2 ) ) are

most a countable number of disjoint measurable sets of non - zero 6 - measure ...

This implies that fı and f2 are

**equal**u - almost everywhere if and only if ( ( A ( 41 )) and ( ( A ( { 2 ) ) are

**equal**. Now the o - finite space ( T , E1 , 0 ) can contain atmost a countable number of disjoint measurable sets of non - zero 6 - measure ...

Page 347

( b ) Show that L ( S , E , u ) is

countable collection of atoms of finite measure { En } in such that every

measurable subset of S - UC _ En is either an atom of infinite measure or a null

set . 50 Show that ...

( b ) Show that L ( S , E , u ) is

**equivalent**to l , if and only if there exists acountable collection of atoms of finite measure { En } in such that every

measurable subset of S - UC _ En is either an atom of infinite measure or a null

set . 50 Show that ...

Page 575

PROOF . Let leo , and suppose that 2 ¢ o ( T . ) . Then there exists a bounded

linear operator A in the space Xo such that ( 21 - T ) Ax = A ( 11 – T ) x = x for x e

Xo . Let the function g be

( a ...

PROOF . Let leo , and suppose that 2 ¢ o ( T . ) . Then there exists a bounded

linear operator A in the space Xo such that ( 21 - T ) Ax = A ( 11 – T ) x = x for x e

Xo . Let the function g be

**equal**to zero for u in a neighborhood of o , and**equal**to( a ...

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### Contents

Metric Spaces | 19 |

Convergence and Uniform Convergence of Generalized | 26 |

Exercises | 33 |

Copyright | |

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