## Linear Operators, Part 2 |

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Page 932

Let S be an abstract set and E a field ( resp . o - field ) of subsets of S . Let F be an

operators on a Hilbert space H satisfying F ( 0 ) = 0 and F ( S ) = 1 . Then there

exists ...

Let S be an abstract set and E a field ( resp . o - field ) of subsets of S . Let F be an

**additive**( resp . weakly countably**additive**) function on to the set of positiveoperators on a Hilbert space H satisfying F ( 0 ) = 0 and F ( S ) = 1 . Then there

exists ...

Page 958

Hence if e , and ex are disjoint then yle , u ez ) = E ( e , u ez ) y ( e , u ez ) = [ E ( e

) + E ( ez ) ] yle , u e ) = E ( e ) y ( e , u ez ) + E ( ez ) y ( e , u ey ) = yle ) + ylez ) , so

that the vector valued set function y is

Hence if e , and ex are disjoint then yle , u ez ) = E ( e , u ez ) y ( e , u ez ) = [ E ( e

) + E ( ez ) ] yle , u e ) = E ( e ) y ( e , u ez ) + E ( ez ) y ( e , u ey ) = yle ) + ylez ) , so

that the vector valued set function y is

**additive**on Bo . Therefore , if ez nez = $ ...Page 1803

Solid analytical geometry and determinants . H . Holt Co . , New York , 1930 .

Dubrovskii ( Doubrovsky ) , V . M . 1 . On some properties of completely

set functions and their application to generalization of a theorem of Lebesgue .

Mat .

Solid analytical geometry and determinants . H . Holt Co . , New York , 1930 .

Dubrovskii ( Doubrovsky ) , V . M . 1 . On some properties of completely

**additive**set functions and their application to generalization of a theorem of Lebesgue .

Mat .

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### Contents

BAlgebras | 859 |

Commutative BAlgebras | 868 |

Commutative BAlgebras | 874 |

Copyright | |

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