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### A counterexample on generalized convolutions

Colloquium Mathematicum

### A Gauss-Kuzmin-Lévy theorem for a certain continued fraction.

International Journal of Mathematics and Mathematical Sciences

Kybernetika

### A noncompact Choquet theorem

Commentationes Mathematicae Universitatis Carolinae

### A Note on Quasicontinuous Kernels Representing Quasi-Linear Positive Maps.

Forum mathematicum

### A probabilistic ergodic decomposition result

Annales de l'I.H.P. Probabilités et statistiques

Let $\left(X,𝔛,\mu \right)$ be a standard probability space. We say that a sub-σ-algebra $𝔅$ of $𝔛$decomposes μ in an ergodic way if any regular conditional probability ${}^{𝔅}\phantom{\rule{-0.166667em}{0ex}}\phantom{\rule{-0.166667em}{0ex}}P$ with respect to $𝔅$ andμ satisfies, for μ-almost every x∈X, $\forall B\in 𝔅,{}^{𝔅}\phantom{\rule{-0.166667em}{0ex}}\phantom{\rule{-0.166667em}{0ex}}P\left(x,B\right)\in \left\{0,1\right\}$. In this case the equality $\mu \left(·\right)={\int }_{X}{}^{𝔅}\phantom{\rule{-0.166667em}{0ex}}\phantom{\rule{-0.166667em}{0ex}}P\left(x,·\right)\mu \left(\mathrm{d}x\right)$, gives us an integral decomposition in “$𝔅$-ergodic” components. For any sub-σ-algebra $𝔅$ of $𝔛$, we denote by $\overline{𝔅}$ the smallest sub-σ-algebra of $𝔛$ containing $𝔅$ and the collection of all setsAin $𝔛$ satisfyingμ(A)=0. We say that $𝔅$ isμ-complete if $𝔅=\overline{𝔅}$. Let $\left\{{𝔅}_{i}i\in I\right\}$ be a non-empty family...

### A property of doubly stochastic densities

Acta Universitatis Carolinae. Mathematica et Physica

Stochastica

### A remark on Slutsky's theorem

Séminaire de probabilités de Strasbourg

### A solution of an equation for indexed functions

Acta Universitatis Carolinae. Mathematica et Physica

### A version of the strong law of large numbers universal under mappings

Mathematica Slovaca

### About the density of spectral measure of the two-dimensional SaS random vector

Discussiones Mathematicae Probability and Statistics

In this paper, we consider a symmetric α-stable p-sub-stable two-dimensional random vector. Our purpose is to show when the function $exp-\left(|a|p+{|b|p\right)}^{\alpha /p}$ is a characteristic function of such a vector for some p and α. The solution of this problem we can find in , in the language of isometric embeddings of Banach spaces. Our proof is based on simple properties of stable distributions and some characterization given in .

### An addendum to a remark on Slutsky's theorem

Séminaire de probabilités de Strasbourg

### An Alpern tower independent of a given partition

Colloquium Mathematicae

Given a measure-preserving transformation T of a probability space (X,ℬ,μ) and a finite measurable partition ℙ of X, we show how to construct an Alpern tower of any height whose base is independent of the partition ℙ. That is, given N ∈ ℕ, there exists a Rokhlin tower of height N, with base B and error set E, such that B is independent of ℙ, and TE ⊂ B.

### An application of a functional equation to information theory

Annales Polonici Mathematici

Kybernetika

### An integral representation of randomized probabilities and its applications

Séminaire de probabilités de Strasbourg

### Approximate dilations

Compositio Mathematica

### Atoms of characteristic measures

Colloquium Mathematicum

### Bernoulli sequences and Borel measurability in $\left(0,1\right)$

Commentationes Mathematicae Universitatis Carolinae

The necessary and sufficient condition for a function $f:\left(0,1\right)\to \left[0,1\right]$ to be Borel measurable (given by Theorem stated below) provides a technique to prove (in Corollary 2) the existence of a Borel measurable map $H:{\left\{0,1\right\}}^{ℕ}\to {\left\{0,1\right\}}^{ℕ}$ such that $ℒ\left(H\left({\mathbf{\text{X}}}^{p}\right)\right)=ℒ\left({\mathbf{\text{X}}}^{1/2}\right)$ holds for each $p\in \left(0,1\right)$, where ${\mathbf{\text{X}}}^{p}=\left({X}_{1}^{p},{X}_{2}^{p},...\right)$ denotes Bernoulli sequence of random variables with $P\left[{X}_{i}^{p}=1\right]=p$.

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