## Linear Operators, Part 2 |

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Page 940

Finally , to see that u ( E ) = u ( E - 1 ) let the

equation 2 ( E ) = u ( E- ) . Then 2 ( G ) = 1 and 2 ( E ) ... Furthermore since the

map s → 8-1 is a homeomorphism in G the

therefore ...

Finally , to see that u ( E ) = u ( E - 1 ) let the

**measure**1 on Ebe defined by theequation 2 ( E ) = u ( E- ) . Then 2 ( G ) = 1 and 2 ( E ) ... Furthermore since the

map s → 8-1 is a homeomorphism in G the

**measure**2 is regular . It followstherefore ...

Page 1130

If we regard N as a

as carrying its ordinary Borel - Lebesgue

establish that ...

If we regard N as a

**measure**space , each integer having**measure**1 , and [ 0 , 1 ]as carrying its ordinary Borel - Lebesgue

**measure**, we may regard A as a**measure**space , carrying the product**measure**v . Our first step will be toestablish that ...

Page 1913

II1.9.7 ( 169 ) , III.9.28 ( 171 ) Measurable set , definition , III.4.3 ( 126 )

See also Set function ) Borel or Borel - Lebesgue , ( 139 ) Borel - Stieltjes , ( 142 )

decomposition of . ( See Decomposition ) determined by a function , ( 142 ) ...

II1.9.7 ( 169 ) , III.9.28 ( 171 ) Measurable set , definition , III.4.3 ( 126 )

**Measure**. (See also Set function ) Borel or Borel - Lebesgue , ( 139 ) Borel - Stieltjes , ( 142 )

decomposition of . ( See Decomposition ) determined by a function , ( 142 ) ...

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### Contents

BAlgebras | 859 |

Bounded Normal Operators in Hilbert Space | 887 |

Miscellaneous Applications | 937 |

Copyright | |

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