Related papers: A unified approach to mass transference principle …

In this short note, we show that, in any given metric space, every Lipschitz open-map image of every subset of a given metric space whose boundary is Hausdorff-null is Hausdorff-measurable with respect to the same dimension. The main…

We apply thermodynamic formalism to a generalized horseshoe map. We prove that a tailored anisotropic Banach space with weighted norms yields a spectral gap for the transfer operator, implying the existence of a unique physical measure.…

We study the class of transversal submanifolds. We characterize their blow-ups at transversal points and prove a negligibility theorem for their "generalized characteristic set", with respect to the Carnot-Carath\'eodory Hausdorff measure.…

Heisenberg's uncertainty principle was originally posed for the limit of the accuracy of simultaneous measurement of non-commuting observables as stating that canonically conjugate observables can be measured simultaneously only with the…

For a given metric measure space $(X,d,\mu)$ we consider finite samples of points, calculate the matrix of distances between them and then reconstruct the points in some finite-dimensional space using the multidimensional scaling (MDS)…

We give a sharp Hausdorff content estimate for the size of the accessible boundary of any domain in a metric measure space of controlled geometry, i.e., a complete metric space equipped with a doubling measure supporting a $p$-Poincar\'e…

The transference theory for Lp spaces of Calderon, Coifman, and Weiss is a powerful tool with many applications to singular integrals, ergodic theory, and spectral theory of operators. Transference methods afford a unified approach to many…

Transfer learning has emerged as a highly sought-after and actively pursued research area within the statistical community. The core concept of transfer learning involves leveraging insights and information from auxiliary datasets to…

In this paper, we study the weighted $n$-dimensional badly approximable points on manifolds. Given a $C^n$ differentiable non-degenerate submanifold $\mathcal{U} \subset \mathbb{R}^n$, we will show that any countable intersection of the…

We extend the Khintchine transference inequalities, as well as a homogeneous-inhomogeneous transference inequality for lattices, due to Bugeaud and Laurent, to a weighted setting. We also provide applications to inhomogeneous Diophantine…

This is the first of two papers describing the process of fitting experimental data under interval uncertainty. Here I present the methodology, designed from the very beginning as an interval-oriented tool, meant to replace to the large…

This paper is a continuation of the paper [Got25] and studies Goldstern's principle, a principle about unions of continuum many null sets, further. The main result is that the Hausdorff measure version of Goldstern's principle for…

We define a one-parameter family of entropies, each assigning a real number to any probability measure on a compact metric space (or, more generally, a compact Hausdorff space with a notion of similarity between points). These entropies…

The quantum multiparameter estimation is very different from the classical multiparameter estimation due to Heisenberg's uncertainty principle in quantum mechanics. When the optimal measurements for different parameters are incompatible,…

We establish a strong law of large numbers and a central limit theorem in the Bures-Wasserstein space of covariance operators -- or equivalently centred Gaussian measures -- over a general separable Hilbert space. Specifically, we show that…

Let $\psi:\mathbb{N}\rightarrow\mathbb{R}_+$ be a monotonically non-increasing function, and let $\psi_v:\mathbb{N}\rightarrow\mathbb{R}_+$ be defined by $\psi_v(q)=1/q^v$. In this article, we consider self-similar sets whose iterated…

Furstenberg, Katznelson and Weiss proved in the early 1980s that every measurable subset of the plane with positive density at infinity has the property that all sufficiently large real numbers are realised as the Euclidean distance between…

For a map $T \colon [0,1] \to [0,1]$ with an invariant measure $\mu$, we study, for a $\mu$-typical $x$, the set of points $y$ such that the inequality $|T^n x - y| < r_n$ is satisfied for infinitely many $n$. We give a formula for the…

We study the fractal pointwise convergence for the equation $i\hbar\partial_tu + P(D)u = 0$, where the symbol $P$ is real, homogeneous and non-singular. We prove that for initial data $f\in H^s(\mathbb{R}^n)$ with $s>(n-\alpha+1)/2$ the…

Following an approach presented by N. Frantzikinakis, B. Host and B. Kra, we show that the parameters in the multidimensional Szemer\'edi theorem for closest integer polynomials have non-empty intersection with the set of shifted primes…