## Linear Operators: Spectral theory |

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Page 1152

The existence of an invariant

countability was first shown by Haar [ 1 ] , and the ... Other results concerning

The existence of an invariant

**measure**on a group satisfying the second axiom ofcountability was first shown by Haar [ 1 ] , and the ... Other results concerning

**measures**invariant under transformations are found in Oxtoby and Ulam [ 1 ] .Page 1153

Since the

integration as developed in Chapter III may be used as a basis for the theory

developed in Sections 3 — 4 . In particular we should notice that the product

group ...

Since the

**measure**space ( R , E , a ) is a o - finite**measure**space the theory ofintegration as developed in Chapter III may be used as a basis for the theory

developed in Sections 3 — 4 . In particular we should notice that the product

group ...

Page 1154

( ii ) o - compact group R and let à be a Haar

= RX R is locally compact and o - compact , it has a Haar

on ...

( ii ) o - compact group R and let à be a Haar

**measure**in R . Then the product**measure**à xa is a Haar**measure**in RX R . Proof . Since the product group R ( 2 )= RX R is locally compact and o - compact , it has a Haar

**measure**2 ( 2 ) definedon ...

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### Contents

IX | 859 |

Eigenvalues and Eigenvectors | 903 |

Spectral Representation | 911 |

Copyright | |

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