相关论文: A version of Marstrand's theorem on a discrete met…
In this paper we prove two general results related to Marstrand's projection theorem in a quite general formulation over separable metric spaces under a suitable transversality hypothesis (the "projections" are in principle only measurable)…
In this paper we make some observations concerning m-metric spaces and point out some discrepancies in the proofs found in the literature. To remedy this, we propose a new topological construction and prove that it is in fact a…
We prove the following variant of Marstrand's theorem about projections of cartesian products of sets: Consider the space $\Lambda_m=\set{(t,O), t\in\R, O\in SO(m)}$ with the natural measure and set…
We present variations on theorems of Mertens as special cases of Density Hypothesis. Moreover, we study a Serre's estimate concerning Lang-Weil estimate.
We discuss discrete Morrey spaces and their generalizations, and we prove necessary and sufficient conditions for the inclusion property among these spaces through an estimate for the characteristic sequences.
The counting and (upper) mass dimensions are notions of dimension for subsets of $\mathbb{Z}^d$. We develop their basic properties and give a characterization of the counting dimension via coverings. In addition, we prove Marstrand-type…
In this paper we prove using quite elementary methods, with a combinatorial nature, two general results related to Marstrand's projection theorem in a quite general formulation over metric spaces under a suitable transversality condition…
We propose a novel measure of statistical depth, the metric spatial depth, for data residing in an arbitrary metric space. The measure assigns high (low) values for points located near (far away from) the bulk of the data distribution,…
In this work we extend many classical results concerning the relationship between densities, tangents and rectifiability to the parabolic spaces, namely $\mathbb{R}^{n+1}$ equipped with parabolic dilations. In particular we prove a…
We prove the following variant of Marstrand's theorem about projections of cartesian products of sets: Let $K_1,...,K_n$ Borel subsets of $\mathbb R^{m_1},... ,\mathbb R^{m_n}$ respectively, and $\pi:\mathbb R^{m_1}\times...\times\mathbb…
In this letter we briefly investigate the mathematical structure of space-time in the framework of discretization. It is shown that the discreteness of space-time may result in a new mechanical system which differ from the usual quantum…
We introduce a new intrinsic metric in subdomains of a metric space and give upper and lower bounds for it in terms of well-known metrics. We also prove distortion results for this metric under quasiregular maps.
We consider mappings satisfying an upper bound for the distortion of families of curves. We establish lower bounds for the distortion of distances under such mappings. As applications, we obtain theorems on the discreteness of the limit…
In this paper, we establish some fixed point theorems in ordered partial metric spaces. An example is given to illustrate our obtained results.
The aim of this text is to extend the theory of generalized ordinary differential equations to the setting of metric spaces. We present existence and uniqueness theorems that significantly improve previous results even when restricted back…
In this paper, we give an interesting extension of the partial S-metric space which was introduced [4] to the M_s-metric space. Also, we prove the existence and uniqueness of a fixed point for a self mapping on an Ms-metric space under…
We provide a short proof that the Wasserstein distance between the empirical measure of a n-sample and the estimated measure is of order n^-(1/d), if the measure has a lower and upper bounded density on the d-dimensional flat torus.
We show that if a non-trivial measure in the plane admits, at almost every point, positive and finite $\alpha$-dimensional density with respect to some norm, then $\alpha$ must be an integer.
This paper presents a new variation of Tverberg's theorem. Given a discrete set $S$ of $R^d$, we study the number of points of $S$ needed to guarantee the existence of an $m$-partition of the points such that the intersection of the $m$…
This is an exposition of the theory of differentiable structures on metric measures spaces, in the sense of Cheeger and Keith.