## Linear Operators: Spectral theory |

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Page 1211

... of S and the real number system R which is

product of v and the measure

every bounded Borel set e of reals and every F in L2(

W(s, ...

... of S and the real number system R which is

**measurable**with respect to theproduct of v and the measure

**u**= (E(-)g, g), and which has the property that forevery bounded Borel set e of reals and every F in L2(

**u**) we have (i) 19-ess ops |W(s, ...

Page 1218

The following lemma is, in the case of scalar functions, a well known theorem of

Lusin. 17 LEMMA. Let u be a finite positive regular measure on the Borel sets of a

topological space R. Then, for every B-space valued

The following lemma is, in the case of scalar functions, a well known theorem of

Lusin. 17 LEMMA. Let u be a finite positive regular measure on the Borel sets of a

topological space R. Then, for every B-space valued

**u**-**measurable**function f on ...Page 1221

Thus a, is the intersection of a sequence of measurable sets, and it follows that o,

is

the theorem, suppose that the functions Wi(., A), ..., W,(., A) are not linearly ...

Thus a, is the intersection of a sequence of measurable sets, and it follows that o,

is

**u**-**measurable**, completing the proof of statement (i). To complete the proof ofthe theorem, suppose that the functions Wi(., A), ..., W,(., A) are not linearly ...

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### Contents

SPECTRAL THEORY | 858 |

Bounded Normal Operators in Hilbert Space | 887 |

Miscellaneous Applications | 937 |

Copyright | |

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