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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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