Related papers: Some remarks about Cantor sets
The paper discusses some uniqueness sets for Fourier series.
This paper is an investigation into Cantor works about representing a function with trigonometric series, and his proofs about its uniqueness. These works are important, because they cause invention of point-set topology, and foundation of…
The existence of two different Cantor sets, one of them contained in the set of Liouville numbers and the other one inside the set of Diophantine numbers, is proved. Finally, a necessary and sufficient condition for the existence of a…
We provide the first examples of finitely generated simple groups that are amenable (and infinite). This follows from a general existence result on invariant states for piecewise-translations of the integers. The states are obtained by…
The main result is that the celebrated Guthrie-Nymann's Cantorval has comeager set of uniqueness. On the other hand many other Cantorvals have meager set of uniqueness.
Here I share a few notes I used in various course lectures, talks, etc. Some may be just calculations that in the textbooks are more complicated, scattered, or less specific; others may be simple observations I found useful or curious.
These notes, connected to a "potpourri" topics class currently underway, discuss some basic topics in analysis and connections with other areas of mathematics.
Cantor sets in \(\mathbb{R}\) are common examples of sets for which Hausdorff measures can be positive and finite. However, there exist Cantor sets for which no Hausdorff measure is supported and finite. The purpose of this paper is to try…
The aim of this note is to show the existence of a large family of Cantorvals arising in the projection description of primitive two-letter substitutions. This provides a common and naturally occurring class of Cantorvals.
We present some new lower bound estimates for certain numbers in Laver table theory and introduce several related structures of interest.
A general theorem on fibers of singular sets is presented.
Alternative approaches to Lebesgue integration are considered.
A brief summary on the properties of the so called Joint Spectral Radius
This is an expository paper detailing some of the recent advances on the problem, with emphasis on the number-theoretic method developed in my paper with Bond and Volberg for rational product sets (arXiv:1109.1031).
A class of Cantor-type spaces and related geometric structures are discussed.
The purpose of this note is twofold. In the first part we observe that two finitely generated non-amenable groups are quasi-isometric if and only if they admit topologically orbit equivalent Cantor minimal actions. In particular, free…
When working in NF, [1] there is a sense that there are more non-Cantorian sets than Cantorian sets. But it is not that immediate result as one expects, since they are externally equinumerous, and the qualification "Cantorian" is not…
As suggested by the title, this paper is a survey of recent results and questions on the collection of computably enumerable sets under inclusion. This is not a broad survey but one focused on the author's and a few others' current…
In this paper we study a class of random Cantor sets. We determine their almost sure Hausdorff, packing, box, and Assouad dimensions. From a topological point of view, we also compute their typical dimensions in the sense of Baire category.…
A Cantor set is a non-empty, compact set that has neither interior nor isolated points. In this paper a Cantor set $K\subseteq \mathbb{R}$ is constructed such that every set definable in $(\mathbb{R},<,+,\cdot,K)$ is Borel. In addition, we…