## Proceedings of the International School of Physics "Enrico Fermi.", Volume 72N. Zanichelli, 1979 - Nuclear physics |

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Page 90

Umegaki ' s theory exploits an idea first proposed by Moy [ 19 ] , that the classical

notion of conditional expectation with

understood as a linear map on the algebra of random variables . The expectation

...

Umegaki ' s theory exploits an idea first proposed by Moy [ 19 ] , that the classical

notion of conditional expectation with

**respect**to a Boolean algebra can beunderstood as a linear map on the algebra of random variables . The expectation

...

Page 91

Now A ' , the conditional expectation of A with

constructed as the random variable defined by the condition A ' ( , ) = Exp ( A | XQ

) , if x , e X , i . e . 00 A ' ( 8 ) = { Exp ( 4 ] X . ) , ( 0 , ) . In other words , A ' is constant

...

Now A ' , the conditional expectation of A with

**respect**to the field F ' , may beconstructed as the random variable defined by the condition A ' ( , ) = Exp ( A | XQ

) , if x , e X , i . e . 00 A ' ( 8 ) = { Exp ( 4 ] X . ) , ( 0 , ) . In other words , A ' is constant

...

Page 94

M Similarly , if a system S initially in the state y interacts with a system initially in

the state y , yielding the correlated state Y = ( di , ) « i ® Pi via a unitary

transformation of the product state y 9 , then conditionalizing Py with

the Boolean ...

M Similarly , if a system S initially in the state y interacts with a system initially in

the state y , yielding the correlated state Y = ( di , ) « i ® Pi via a unitary

transformation of the product state y 9 , then conditionalizing Py with

**respect**tothe Boolean ...

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### Contents

Gradual infiltration of probabilitys laws into physical sciences | 1 |

Statistical fluctuations | 10 |

Introduction | 21 |

Copyright | |

24 other sections not shown

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according additive appear applied approach argument assume atoms Borel called classical closed complete concept consider constant corresponding countable course defined definition derived described determined dialog discussion distribution dynamics edited effect elementary elements energy equal equation equivalent example exists experiment expressed fact field final finite formal frequency function geometry give given Hence implies initial interpretation lattice limit logical mass material mathematical means measurement motion natural observable obtain operator particle particular Phys physical positive possible precision present principle probability problem proof propositions proved quantity quantum mechanics question reason refer relation relative represented requirement respect result rules satisfies sense sequence space space-time special relativity statistical structure theorem theory transformation turn unit Universe vector