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On joint distribution in quantum logics. II. Noncompatible observables

Anatolij Dvurečenskij (1987)

Aplikace matematiky

This paper i a continuation of the first part under the same title. The author studies a joint distribution in $σ$ -finite measures for noncompatible observables of a quantum logic defined on some system of $σ$ -independent Boolean sub- $σ$ -algebras of a Boolean $σ$ -algebra. We present some necessary and sufficient conditions fot the existence of a joint distribution. In particular, it is shown that an arbitrary system of obsevables has a joint distribution in a measure iff it may be embedded into a system...

On Kakutani's Dichotomy Theorem for Infinitive Products of not Necessarily Independent Functions.

G. Ritter (1979)

Mathematische Annalen

On Kalmbach measurability

A. B. d' Andrea, P. de Lucia, John David Maitland Wright (1994)

Applications of Mathematics

In this note we show that, for an arbitrary orthomodular lattice $L$ , when $μ$ is a faithful, finite-valued outer measure on $L$ , then the Kalmbach measurable elements of $L$ form a Boolean subalgebra of the centre of $L$ .

On Kantorovich's result on the symmetry of Dini derivatives

Martin Koc, Luděk Zajíček (2010)

Commentationes Mathematicae Universitatis Carolinae

For $f : (a, b) \to ℝ$ , let $A_{f}$ be the set of points at which $f$ is Lipschitz from the left but not from the right. L.V. Kantorovich (1932) proved that, if $f$ is continuous, then $A_{f}$ is a “( $k_{d}$ )-reducible set”. The proofs of L. Zajíček (1981) and B.S. Thomson (1985) give that $A_{f}$ is a $σ$ -strongly right porous set for an arbitrary $f$ . We discuss connections between these two results. The main motivation for the present note was the observation that Kantorovich’s result implies the existence of a $σ$ -strongly right porous set $A \subset (a, b)$ ...

On lattices and algebras of simple functions

Yurij Aleksandrovich Abramovich, Zbigniew Lipecki (1990)

Commentationes Mathematicae Universitatis Carolinae

On lattice-topological properties of general Wallman spaces.

Vlad, Carmen (1998)

International Journal of Mathematics and Mathematical Sciences

On lifting quasi-Radon measures.

Malyugin, S.A. (2001)

Sibirskij Matematicheskij Zhurnal

On Lindelöf lattices and separation.

Eid, George M. (1991)

International Journal of Mathematics and Mathematical Sciences

On Marczewski-Burstin representable algebras

Marek Balcerzak, Artur Bartoszewicz, Piotr Koszmider (2004)

Colloquium Mathematicae

We construct algebras of sets which are not MB-representable. The existence of such algebras was previously known under additional set-theoretic assumptions. On the other hand, we prove that every Boolean algebra is isomorphic to an MB-representable algebra of sets.