We construct a sequence of continuous functions (hn) on any given uncountable Polish space, such that ∑ hn is divergent everywhere, but for any sign sequence (εn) ∈ {−1,+1} N which contains infinitely many −1 and +1 the series ∑ εnhn is convergent at at least one point. We can even have hn → 0, and if we take our given Polish space to be any uncountable closed subset of R, we can require that e...

We study the probability theory of countable dense random subsets of (uncountably infinite) Polish spaces. It is shown that if such a set is stationary with respect to a transitive (locally compact) group of symmetries then any event which concerns the random set itself (rather than accidental details of its construction) must have probability zero or one. Indeed the result requires only quasi-...

We introduce a model of the set of all Polish (=separable complete metric) spaces which is the cone R of distance matrices, and consider the geometrical and probabilistic problems connected with this object. We prove that the generic Polish space in the sense of this model is the so called universal Urysohn space which was defined by P.S.Urysohn in the 1920-th. Then we consider the metric space...

For locally compact groups all actions on a standard measure algebra have a spatial realization. For many Polish groups this is no longer the case. However, we show here that for non-archimedean Polish groups all measure algebra actions do have spatial realizations. In the other direction we show that an action of a Polish group is whirly (“ergodic at the identity”) if and only if it admits no ...

In simulation, Median Polish Kriging is a technique used to predict unobserved data points in two-dimensional space. The linear behavior of the traditional Median Polish Kriging in the estimation of the mean function in a high grid makes the interpolation of O(1) which has a low order in the prediction and that leads to a high prediction error. Therefore, an improvement in the estimation of the...

It is shown that for every Polish group G that is not locally compact there is a continuous action a of G on a Π1-complete subset A of a Polish space X such that a cannot be extended to any superset of A in X. This answers a question posed by Becker and Kechris and shows that an earlier theorem of them is optimal in several aspects.

We show that for any sufficiently homogeneous metrizable compactum X there is a Polish group G acting continuously on the space of rational numbersQ such that X is its unique G-compactification. This allows us to answer Problem 995 in the ‘Open Problems in Topology II’ book in the negative: there is a one-dimensional Polish groupG acting transitively onQ forwhich theHilbert cube is its uniqueG-...

the aim of the current investigation was to evaluate the sedentary lifestyle of the polish population and its link with prolonged sitting in light of individual and environmental factors.the sample consisted of 1505 polish people between 18 and 64 years old. the computer-assisted telephone interview (cati) survey was conducted with the polish version of international physical activity questionn...