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

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Page 354

3'1. Failure of the probability axioms. - Let the actual long run be counted in days:

1 (today), 2 (tomorrow), and so on. Let A(n) be an event that happens only on the

n-th day. Then the limit of the

3'1. Failure of the probability axioms. - Let the actual long run be counted in days:

1 (today), 2 (tomorrow), and so on. Let A(n) be an event that happens only on the

n-th day. Then the limit of the

**relative frequency**of the occurrence of A(n) in the ...Page 377

Conditional

(^l B) undefined when P(B) = 0. This is in contrast with earlier theories of

probability, and also somewhat in contrast with common intuitions. The

probability of ...

Conditional

**relative frequencies**[16]. The standard (Kolmogoroff) theory leaves P(^l B) undefined when P(B) = 0. This is in contrast with earlier theories of

probability, and also somewhat in contrast with common intuitions. The

probability of ...

Page 378

Thus we have an example of a well-defined

zero antecedent », that is on an event which itself has

There have been several efforts to develop theories of probability with P(AjB) ...

Thus we have an example of a well-defined

**relative frequency**conditional on a «zero antecedent », that is on an event which itself has

**relative frequency**zero.There have been several efforts to develop theories of probability with P(AjB) ...

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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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3-geometry algebra applied assertion atoms axioms Boolean Borel field Borel sets calculus concept conditional probability conditionalization consider corresponding countable course defined definition denote derived deterministic dialog dialog-game disjoint dynamics edited Einstein elements equation equivalent exists experiment finite formal function geometry given Gleason's theorem Hence Hilbert space implies induction initial interaction interpretation irreversible Journ linear magnitude Math mathematical means Neumann non-Boolean notion observable orthogonal orthomodular lattice particle photon Phys physical quantity physical system physical theories physicists positive precision probabilistic probability measure probability space probability theory problem procedure quantum logic quantum mechanics quantum theory quantum-logical question radioactive random variable real numbers relation relative frequency relf represented respect result rule sequence space-time special relativity spin statistical operator subset subspace superspace theorem tion transformation truth universal constants vector velocity von Neumann algebra zero