## Linear Operators: General theory |

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Page 193

By

this case the desired conclusion was established in Corollary 8 . Q . E . D . 13

THEOREM . Let ( S , ES , ' ) and ( T , ET , 2 ) be finite measure spaces and let ( R ,

ER ...

By

**Lemma**11 it may be assumed that the measure spaces are positive , but inthis case the desired conclusion was established in Corollary 8 . Q . E . D . 13

THEOREM . Let ( S , ES , ' ) and ( T , ET , 2 ) be finite measure spaces and let ( R ,

ER ...

Page 697

Nelson Dunford, Jacob T. Schwartz, William G. Bade. 11

be a positive measure space and let { T ( 4 , . . . , tx ) , tz , . . . , tx > 0 } be a strongly

measurable semi - group of operators in L ( S , E , u ) with \ T ( tj , . . . , tk ) 1 = 1 ...

Nelson Dunford, Jacob T. Schwartz, William G. Bade. 11

**LEMMA**. Let ( S , E , u )be a positive measure space and let { T ( 4 , . . . , tx ) , tz , . . . , tx > 0 } be a strongly

measurable semi - group of operators in L ( S , E , u ) with \ T ( tj , . . . , tk ) 1 = 1 ...

Page 699

Q . E . D . We shall now state and prove the

technical reasons occurring later the following

called a positive sub - semi - group rather than for a positive semi - group . The

proof of ...

Q . E . D . We shall now state and prove the

**lemma**referred to as CPx . Fortechnical reasons occurring later the following

**lemma**is stated for what might becalled a positive sub - semi - group rather than for a positive semi - group . The

proof of ...

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### Contents

Metric Spaces | 19 |

Convergence and Uniform Convergence of Generalized | 26 |

Exercises | 33 |

Copyright | |

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