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On locally solid topological lattice groups

Abdul Rahim Khan, Keith Rowlands (2007)

Czechoslovak Mathematical Journal

Let ( G , τ ) be a commutative Hausdorff locally solid lattice group. In this paper we prove the following: (1) If ( G , τ ) has the A (iii)-property, then its completion ( G ^ , τ ^ ) is an order-complete locally solid lattice group. (2) If G is order-complete and τ has the Fatou property, then the order intervals of G are τ -complete. (3) If ( G , τ ) has the Fatou property, then G is order-dense in G ^ and ( G ^ , τ ^ ) has the Fatou property. (4) The order-bound topology on any commutative lattice group is the finest locally solid topology on...

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.

On measure-preserving transformations and doubly stationary symmetric stable processes

A. Gross, A. Weron (1995)

Studia Mathematica

In a 1987 paper, Cambanis, Hardin and Weron defined doubly stationary stable processes as those stable processes which have a spectral representation which is itself stationary, and they gave an example of a stationary symmetric stable process which they claimed was not doubly stationary. Here we show that their process actually had a moving average representation, and hence was doubly stationary. We also characterize doubly stationary processes in terms of measure-preserving regular set isomorphisms...

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