This book is the first systematic treatment of measures on projection lattices of von Neumann
algebras. It presents significant recent results in this field. One part is inspired by the …

It is shown that, given any finite set of pairs of random events in a Boolean algebra which are
correlated with respect to a fixed probability measure on the algebra, the algebra can be …

The common cause principle says that every correlation is either due to a direct causal effect
linking the correlated entities or is brought about by a third factor, a so-called common …

If A (V) is a net of local von Neumann algebras satisfying standard axioms of algebraic
relativistic quantum field theory and V 1 and V 2 are spacelike separated spacetime regions …

Reichenbach's principles of a probabilistic common cause of probabilistic correlations is
formulated in terms of relativistic quantum field theory, and the problem is raised whether …

In quantum theory, the modulus-square of the inner product of two normalized Hilbert space
elements is to be interpreted as the transition probability between the pure states …

The notion of common cause closedness of a classical, Kolmogorovian probability space
with respect to a causal independence relation between the random events is defined, and …

In the paper it will be shown that Reichenbach's Weak Common Cause Principle is not valid
in algebraic quantum field theory with locally finite degrees of freedom in general. Namely …

In the paper we investigate statistical independence of C*-algebras and its relation to other
independence conditions studied in operator algebras and quantum field theory. Especially …

Various reconstructions of finite-dimensional quantum mechanics result in a formally real
Jordan algebra A and a last step remains to conclude that A is the self-adjoint part of a C …