## Linear Operators: General theory |

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Page 182

Thus da / du is

uds ) , Ee2 . ... field ) of sets in Sq . For an additive set function Ma on £ , the

equation 4 ( 8 - 4 ( E ) ) = M2 ( E )

Moreover ...

Thus da / du is

**defined**u - almost everywhere by the formula 2 ( E ) = S , 7 ( - )uds ) , Ee2 . ... field ) of sets in Sq . For an additive set function Ma on £ , the

equation 4 ( 8 - 4 ( E ) ) = M2 ( E )

**defines**an additive set function My on Ex .Moreover ...

Page 240

It is evident that if we

and u ( d ) = 0 ... The space B ( S ) is

all bounded scalar functions on S . The norm is given by W = sup \ | ( s ) ] . 14 .

It is evident that if we

**define**the set function u on & by placing u ( E ) = 0 if E + 6and u ( d ) = 0 ... The space B ( S ) is

**defined**for an arbitrary set S and consists ofall bounded scalar functions on S . The norm is given by W = sup \ | ( s ) ] . 14 .

Page 241

u , S ) . 18 . The space L ( S , E , u ) is

and any positive measure space ( S , E , ) . It consists of those u - measurable ...

**defined**on the o - field B of all Borel sets in S . The norm ul is the total variation v (u , S ) . 18 . The space L ( S , E , u ) is

**defined**for any real number p , 13p < 0 ,and any positive measure space ( S , E , ) . It consists of those u - measurable ...

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### Contents

Special Spaces | 237 |

Convex Sets and Weak Topologies | 409 |

General Spectral Theory | 555 |

Copyright | |

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