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

Andrew Yingst (2014)

Colloquium Mathematicae

Consider an experiment with d+1 possible outcomes, d of which occur with probabilities x ₁ , . . . , 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 x ₁ , . . . , 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 regular averaging operators and its consequences

Spiros A. Argyros, Alexander D. Arvanitakis (2002)

Studia Mathematica

We present a characterization of continuous surjections, between compact metric spaces, admitting a regular averaging operator. Among its consequences, concrete continuous surjections from the Cantor set 𝓒 to [0,1] admitting regular averaging operators are exhibited. Moreover we show that the set of this type of continuous surjections from 𝓒 to [0,1] is dense in the supremum norm in the set of all continuous surjections. The non-metrizable case is also investigated. As a consequence, we obtain...

A characterization of space-filling curves.

Gaspar Mora, Juan A. Mira (2002)

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 tribes with respect to the Łukasiewicz t -norm

Erich Peter Klement, Mirko Navara (1997)

Czechoslovak Mathematical Journal

We give a complete characterization of tribes with respect to the Łukasiewicz t -norm, i. e., of systems of fuzzy sets which are closed with respect to the complement of fuzzy sets and with respect to countably many applications of the Łukasiewicz t -norm. We also characterize all operations with respect to which all such tribes are closed. This generalizes the characterizations obtained so far for other fundamental t -norms, e. g., for the product t -norm.

A Characterization of Uniform Distribution

Joanna Chachulska (2005)

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 class of continua that are not attractors of any IFS

Marcin Kulczycki, Magdalena Nowak (2012)

Open Mathematics

This paper presents a sufficient condition for a continuum in ℝn to be embeddable in ℝn in such a way that its image is not an attractor of any iterated function system. An example of a continuum in ℝ2 that is not an attractor of any weak iterated function system is also given.

A complete characterization of R-sets in the theory of differentiation of integrals

G. A. Karagulyan (2007)

Studia Mathematica

Let s be the family of open rectangles in the plane ℝ² with a side of angle s to the x-axis. We say that a set S of directions is an R-set if there exists a function f ∈ L¹(ℝ²) such that the basis s differentiates the integral of f if s ∉ S, and D ̅ s f ( x ) = l i m s u p d i a m ( R ) → 0 , x ∈ R ∈ s | R | - 1 ∫ R f = ∞ almost everywhere if s ∈ S. If the condition D ̅ s f ( x ) = ∞ holds on a set of positive measure (instead of a.e.) we say that S is a WR-set. It is proved that S is an R-set (resp. a WR-set) if and only if it is a G δ (resp. a G δ σ ).

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