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

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Page 90

An extension of classical probability theory to noncommutative algebras of

by Umegaki [17] and generalized in certain ways by Da vies and Lewis [18].

An extension of classical probability theory to noncommutative algebras of

**random variables**, i.e. to non-Boolean possibility structures, has been developedby Umegaki [17] and generalized in certain ways by Da vies and Lewis [18].

Page 91

of X, i.e. the A'ej represent the new atomic events of the field which may be

understood as labelled by the possible values of a magnitude E. The conditional

expectation of the

where ...

of X, i.e. the A'ej represent the new atomic events of the field which may be

understood as labelled by the possible values of a magnitude E. The conditional

expectation of the

**random variable**A on the event e, is ExP (A\X.) = ZA(xj)-f±-where ...

Page 92

MOT pointed out [20] that, if we fix the field &' , then classical conditional- ization

with respect to &' defines a map on the commutative algebra of

such that each

MOT pointed out [20] that, if we fix the field &' , then classical conditional- ization

with respect to &' defines a map on the commutative algebra of

**random variables**,such that each

**random variable**A is mapped onto A', defined as above.### What people are saying - Write a review

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### Contents

E Amaldi Radioactivity a pragmatic pillar of probabilistic | 1 |

Statistical fluctuations | 10 |

Final remarks | 21 |

Copyright | |

24 other sections not shown

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