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

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Page 31

Let us quote a few significant examples. i) In the historical approach initiated by

BiRKHOFF and

introduced as iP- valued measures on the set (Boolean

...

Let us quote a few significant examples. i) In the historical approach initiated by

BiRKHOFF and

**von Neumann**[2], and ... have the role of derived concepts, beingintroduced as iP- valued measures on the set (Boolean

**algebra**) of all Borel sets...

Page 128

is the

further property is available, namely the fundamental theorem of Gleason [11]: if

dim > 3, then every probability measure on the lattice J"(.5#(jr )) of projectors ...

is the

**von Neumann algebra**&S(jtf) of all bounded operators on jf. In this case afurther property is available, namely the fundamental theorem of Gleason [11]: if

dim > 3, then every probability measure on the lattice J"(.5#(jr )) of projectors ...

Page 129

1, purely lattice theoretically, without reference to noncommutative theory on

algebras, for two reasons at least. The first is that an orthomodular lattice in

general cannot be thought of as the lattice of projections of a

1, purely lattice theoretically, without reference to noncommutative theory on

algebras, for two reasons at least. The first is that an orthomodular lattice in

general cannot be thought of as the lattice of projections of a

**von Neumann****algebra**, ...### 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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### Common terms and phrases

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