Related papers: A survey of recent extensions and generalisations …
In this article we discuss the Mass Transference Principle due to Beresnevich and Velani and survey several generalisations and variants, both deterministic and random. Using a Hausdorff measure analogue of the inhomogeneous…
We introduce a general principle for studying the Hausdorff measure of limsup sets. A consequence of this principle is the well-known Mass Transference Principle of Beresnevich and Velani (2006).
The mass transference principle, proved by Beresnevich and Velani in 2006, is a strong result that gives lower bounds for the Hausdorff dimension of limsup sets of balls. We present a version for limsup sets of open sets of arbitrary shape.
I prove a mass transference principle for general shapes, similar to a recent result by H. Koivusalo and M. Rams. The proof relies on Vitali's covering lemma and manipulations with Riesz energies. The main novelty is that it is proved that…
The mass transference principle, discovered by Beresnevich and Velani [Ann Math (2), 2006], is a landmark result in Diophantine approximation that allows us to obtain the Hausdorff measure theory of $\limsup$ set. Another important tool is…
A generalization of a distribution increases the flexibility particularly in studying of a phenomenon and its properties. Many generalizations of continuous univariate distributions are available in literature. In this study, an…
I briefly discuss some recent developments (and recall some old news) in the theory and phenomenology of generalised parton distributions.
In this article, one investigates in a very general frame mass transference principles from ball to arbitrary open sets when the sequence of balls is distributed according to a finite measure. As an application of the main theorem, a mass…
In this paper we establish a general form of the Mass Transference Principle for systems of linear forms conjectured in [1]. We also present a number of applications of this result to problems in Diophantine approximation. These include a…
Recently, mass transference principles in metric number theory extend towards two direction. On one hand, the shape of the approximating sets can be taken of various shape, balls, rectangles or even general open sets (one refers to some…
In this paper we prove a general form of the Mass Transference Principle for $\limsup$ sets defined via neighbourhoods of sets satisfying a certain local scaling property. Such sets include self-similar sets satisfying the open set…
In this short note we give counterexamples to several results related to extension theorems published recently.
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…
A Hausdorff measure version of the Duffin-Schaeffer conjecture in metric number theory is introduced and discussed. The general conjecture is established modulo the original conjecture. The key result is a Mass Transference Principle which…
There are several extensions of the classical Banach Fixed Point Theorem in technical literature. A branch of generalizations replaces usual contractivity by weaker but still effective assumptions. Our note follows this stream, presenting…
We establish a general transference principle for the irrationality measure of points with $\mathbb{Q}$-linearly independent coordinates in $\mathbb{R}^{n+1}$, for any given integer $n\geq 1$. On this basis, we recover an important…
The mass transference principle of Beresnevich and Velani is a powerful mechanism for determining the Hausdorff dimension/measure of $\limsup$ sets that arise naturally in Diophantine approximation. However, in the setting of dynamical…
We show that the stochastic interpretation of Tsallis' thermostatistics given recently by Beck [Phys. Rev. Lett {\bf 87}, 180601 (2001)] leads naturally to a multi-parameter generalization. The resulting class of distributions is able to…
We provide an introduction to selected recent advances in the mathematical understanding of Einstein's theory of gravitation.
Limit theorems for a random number of independent random variables are frequently called transfer theorems. Investigations into this direction for sums of random variables with independent random sample size have been originated by…