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### A characterization of Jordan and Lebesgue measures

Colloquium Mathematicae

### A characterization of partition polynomials and good Bernoulli trial measures in many symbols

Colloquium Mathematicae

Consider an experiment with d+1 possible outcomes, d of which occur with probabilities $x₁,...,{x}_{d}$. If we consider a large number of independent occurrences of this experiment, the probability of any event in the resulting space is a polynomial in $x₁,...,{x}_{d}$. We characterize those polynomials which arise as the probability of such an event. We use this to characterize those x⃗ for which the measure resulting from an infinite sequence of such trials is good in the sense of Akin.

### A characterization of space-filling curves.

RACSAM

En este artículo revisamos un famoso teorema, descubierto por H. Steinhaus en 1936, en el que se da una condición suficiente que permite obtener las funciones coordenadas de una curva que llena el cuadrado unidad. Ponemos de manifiesto que el recíproco de este teorema no se cumple para la curva de Lebesgue. Aquí proponemos un teorema de caracterización de curvas que llenan el espacio, basado en una condición de llenado. Asimismo, damos una caracterización constructiva de esta condición de llenado...

### A Characterization of Uniform Distribution

Bulletin of the Polish Academy of Sciences. Mathematics

Is the Lebesgue measure on [0,1]² a unique product measure on [0,1]² which is transformed again into a product measure on [0,1]² by the mapping ψ(x,y) = (x,(x+y)mod 1))? Here a somewhat stronger version of this problem in a probabilistic framework is answered. It is shown that for independent and identically distributed random variables X and Y constancy of the conditional expectations of X+Y-I(X+Y > 1) and its square given X identifies uniform distribution either absolutely continuous or discrete....

### A Dieudonné theorem for lattice group-valued measures

Kybernetika

A version of Dieudonné theorem is proved for lattice group-valued modular measures on lattice ordered effect algebras. In this way we generalize some results proved in the real-valued case.

### A measure decomposition theorem

Mathematica Slovaca

### A nonlinear Banach-Steinhaus theorem and some meager sets in Banach spaces

Studia Mathematica

We establish a Banach-Steinhaus type theorem for nonlinear functionals of several variables. As an application, we obtain extensions of the recent results of Balcerzak and Wachowicz on some meager subsets of L¹(μ) × L¹(μ) and c₀ × c₀. As another consequence, we get a Banach-Mazurkiewicz type theorem on some residual subset of C[0,1] involving Kharazishvili's notion of Φ-derivative.

### A note on equivalent interval covering systems for Hausdorff dimension on R.

International Journal of Mathematics and Mathematical Sciences

### A note on the Lebesgue-Darst decomposition theorem.

Acta Mathematica Universitatis Comenianae. New Series

### A note on "Two classes of measures'' (by J. K. Pachl)

Colloquium Mathematicae

### A problem of invariance for Lebesgue measure

Colloquium Mathematicae

### A sequential approach to a construction of measures

Commentationes Mathematicae Universitatis Carolinae

### A set function without $\sigma$-additive extension having finitely additive extensions arbitrarily close to $\sigma$-additivity

Czechoslovak Mathematical Journal

### A short zero-one law proof of a result of Abian.

Aequationes mathematicae

### About $\sigma$-additive and $\sigma$-maxitive measures

Mathematica Slovaca

### Algunos espacios topológicos que admiten una medida-categoría.

Collectanea Mathematica

### Almost sure absolute continuity of Bernoulli convolutions

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

We prove an extension of a result by Peres and Solomyak on almost sure absolute continuity in a class of symmetric Bernoulli convolutions.

### An ${F}_{\sigma }$ semigroup of zero measure which contains a translate of every countable set

Groupe d'étude en théorie analytique des nombres

### An inquiry-based method for Choquet integral-based aggregation of interface usability parameters

Kybernetika

The concept of usability of man-machine interfaces is usually judged in terms of a number of aspects or attributes that are known to be subject to some rough correlations, and that are in many cases given different importance, depending on the context of use of the application. In consequence, the automation of judgment processes regarding the overall usability of concrete interfaces requires the design of aggregation operators that are capable of modeling approximate or ill-defined interactions...

### An intersection property of sets with positive measure

Colloquium Mathematicae

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