## Linear Operators, Part 1 |

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Page 186

... used in proving uniqueness in Lemma 1 goes through without change in this

case . Q.E.D. 3 DEFINITION . The

Theorem 2 is called the product

Mn ) .

... used in proving uniqueness in Lemma 1 goes through without change in this

case . Q.E.D. 3 DEFINITION . The

**measure space**( S , E , u ) constructed inTheorem 2 is called the product

**measure space**of the**measure spaces**( Sn , En ,Mn ) .

Page 188

Q.E.D. As in the case of finite

S , E , u ) constructed in Corollary 6 from the o - finite

) the product

Q.E.D. As in the case of finite

**measure spaces**we shall call the**measure space**(S , E , u ) constructed in Corollary 6 from the o - finite

**measure spaces**( Si , Einpi) the product

**measure space**and write ( S , E , u ) = Ph_ ( Si , Ei , Mi ) . The best ...Page 725

37 Let ( S , E , ) be a positive

transformation of L ( S , E , u ) into itself . Suppose that Ti S l and that there exists

a constant K such that AT , n ) SK . Show that limn700 ( A ( T , n ) f ) ( s ) exists u ...

37 Let ( S , E , ) be a positive

**measure space**, and T a non - negative lineartransformation of L ( S , E , u ) into itself . Suppose that Ti S l and that there exists

a constant K such that AT , n ) SK . Show that limn700 ( A ( T , n ) f ) ( s ) exists u ...

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### Contents

Preliminary Concepts | 1 |

The VitaliHahnSaks Theorem and Spaces of Measures | 7 |

B Topological Preliminaries | 10 |

Copyright | |

87 other sections not shown

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