Related papers: Level sets and the uniqueness of measures
The lens depth of a point has been recently extended to general metric spaces, which is not the case for most depths. It is defined as the probability of being included in the intersection of two random balls centred at two random points X…
In this paper convergence theorems for sequences of scalar, vector and multivalued Pettis integrable functions on a topological measure space are proved for varying measures vaguely convergent.
We show that in a metric space, any continuous function with compact sublevel sets and finite metric slope is uniquely determined by the slope and its critical values.
It is well-known that entire functions whose spectrum belongs to a fixed bounded set $S$ admit real uniformly discrete uniqueness sets $\Lambda$. We show that the same is true for much wider spaces of continuous functions. In particular,…
We first prove that in a sigma-finite von Neumann factor M, a positive element $a$ with properly infinite range projection R_a is a linear combination of projections with positive coefficients if and only if the essential norm ||a||_e with…
In [6], a constraint on invariant measures of bi-permutative cellular automata has been observed: fixed values at the positive indices determine almost-surely a uniform conditional probability on the subset of values of positive conditional…
A result of H. Steinhaus states that any positive Lebesgue measurable set has a property that its difference set contains an open interval around the origin. Y. V. Mospan proved that this result is the characterization of absolutely…
In this paper, motivated by the classical notion of a Strebel qua- dratic differential on a compact Riemann surface without boundary, we in- troduce several classes of quadratic differentials (called non-chaotic, gradient, and positive…
In the paper we study properties of the set of critical points for self-similar sets. We introduce simple condition that implies at most countably many critical values and we construct a self-similar set with uncountable set of critical…
We investigate the size of the distance set determined by two subsets of finite dimensional vector spaces over finite fields. A lower bound of the size is given explicitly in terms of cardinalities of the two subsets. As a result, we…
This paper studies the uniqueness of two non-constant meromorphic functions when they share a finite set. Moreover, we will give the existence of unique range sets for meromorphic functions that are zero sets of polynomials that do not…
We consider diffraction of Delone sets in Euclidean space. We show that the set of Bragg peaks with high intensity is always Meyer (if it is relatively dense). We use this to provide a new characterization for Meyer sets in terms of…
Prior proposals for cumulative statistics suggest making tiny random perturbations to the scores (independent variables in a regression) in order to ensure the scores' uniqueness. Uniqueness means that no score for any member of the…
Many quantities that characterize network elements are defined in an explicit form and calculated directly from the network structure; examples of include several centrality measures like degree, closeness, or betweenness. However, there…
In this paper, we defined three kinds of measures depending on the given finite directed graphs. For the given finite directed graph, we can construct the free semigroupoid, the diagram set and the reduced diagram set, as algebraic…
Recently George Bergman proved that the symmetric group of an infinite set possesses the following property which we call by the {\it universality of finite width}: given any generating set $X$ of the symmetric group of an infinite set…
Some limit theorems of the type $\int_{\Omega}f_n dm_n -- --> \int_{\Omega}f dm$ are presented for scalar, (vector), (multi)-valued sequences of m_n-integrable functions f_n. The convergences obtained, in the vector and multivalued…
Some new results concerning the equation $\sigma(N)=aM, \sigma(M)=bN$ are proved. As a corollary, there are only finitely many odd superperfect numbers with a fixed number of distinct prime factors.
Early results by Borel and Cantelli and Erd\H{o}s and Chung have provided bounds for the measure of a limsup set in terms of measures of its constituent sets and their intersections. Recent work by Beresnevich and Velani \cite{Velanipaper}…
We establish certain topological properties of rank understood as a function on the set of invariant measures on a topological dynamical system. To be exact, we show that rank is of Young class LU (i.e., it is the limit of an increasing…