## Linear Operators, Part 1 |

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Page 164

... non - negative , it follows that { ūn ( E ) } is a bounded non - decreasing set of

real numbers for each E € £ . We define 11 ( E ) = limnīn ( E ) , E € En . By

Corollary 4 , 2 , is countably additive on El , and hence its

S , E ) .

... non - negative , it follows that { ūn ( E ) } is a bounded non - decreasing set of

real numbers for each E € £ . We define 11 ( E ) = limnīn ( E ) , E € En . By

Corollary 4 , 2 , is countably additive on El , and hence its

**restriction**to £ is in ca (S , E ) .

Page 166

Q.E.D. In addition to the

this other type of

Q.E.D. In addition to the

**restriction**of u to a subfield of Ethere is another type of**restriction**of common occurrence in integration theory . ... following discussion ofthis other type of

**restriction**it is not necessary to assume that u is non - negative .Page 168

Then there is a set s , in E , a sub o - field & of E ( S ) , and a closed separable

subspace X of X such that the

( i ) the measure space ( S1 , E1 , M2 ) is o - finite ; ( ii ) the B - space L ( S1 , E1 ...

Then there is a set s , in E , a sub o - field & of E ( S ) , and a closed separable

subspace X of X such that the

**restriction**My of u to ; has the following properties :( i ) the measure space ( S1 , E1 , M2 ) is o - finite ; ( ii ) the B - space L ( S1 , E1 ...

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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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