## 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 RxR ...

Since the

**measure**space ( R , E , 2 ) 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 RxR ...

Page 1154

o - compact group R and let 2 be a Haar

) = RxR is locally compact and o - compact , it has a Haar

on its ...

o - compact group R and let 2 be a Haar

**measure**in R. Then the product**measure**à xà is a Haar**measure**in Rx R. PROOF . Since the product group R ( 2) = RxR is locally compact and o - compact , it has a Haar

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

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Linear Operators, Part 2: Spectral Theory, Self Adjoint Operators in Hilbert ... Nelson Dunford,Jacob T. Schwartz No preview available - 1988 |

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