## Linear Operators: Spectral theory |

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Page 1152

The existence of an invariant

The existence of an invariant

**measure**on a group satisfying the second axiom of countability was first shown by Haar [ 1 ] ... Other results concerning**measures**invariant under transformations are found in Oxtoby and Ulam [ 1 ] .Page 1153

Since the

Since the

**measure**space ( R , E , 2 ) is a o - finite**measure**space the theory of 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 ...Page 1154

D o - compact group R and let à be a Haar

D o - compact group R and let à be a Haar

**measure**in R. Then the product**measure**à x2 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**7 ( 2 ) defined ...### What people are saying - Write a review

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### Contents

BAlgebras | 859 |

Miscellaneous Applications | 937 |

Compact Groups | 945 |

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