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Some remarks about strong proximality of compact flows

A. Bouziad, J.-P. Troallic (2009)

Colloquium Mathematicae

This note aims at providing some information about the concept of a strongly proximal compact transformation semigroup. In the affine case, a unified approach to some known results is given. It is also pointed out that a compact flow (X,𝓢) is strongly proximal if (and only if) it is proximal and every point of X has an 𝓢-strongly proximal neighborhood in X. An essential ingredient, in the affine as well as in the nonaffine case, turns out to be the existence of a unique minimal subset.

Some remarks on duality of stationary sequences

L. Klotz, M. Riedel (2002)

Colloquium Mathematicae

The paper clarifies the connection between Urbanik's and Miamee and Pourahmadi's concepts of duality for univariate weakly stationary random sequences. Some of Urbanik's results are proved in an alternative way and at the same time generalized to the multivariate case.

Some Remarks on Functionals with the Tensorization Property

Paweł Wolff (2007)

Bulletin of the Polish Academy of Sciences. Mathematics

We investigate the subadditivity property (also known as the tensorization property) of φ-entropy functionals and their iterations. In particular we show that the only iterated φ-entropies with the tensorization property are iterated variances. This is a complement to the result due to Latała and Oleszkiewicz on characterization of the standard φ-entropies with the tensorization property.

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