In this paper we introduce and study a certain intricate Cantor-like set C contained in unit interval. Our main result is to show that the set C itself, as well as the set of dissipative points within C, both have Hausdorff dimension equal to 1. The proof uses the transience of a certain non-symmetric Cauchy-type random walk.

In this paper we compute transitive cardinal coefficients of ideals on generalized Cantor spaces. In particular, we observe that there exists a null set A ⊆ 21 such that for every null set B ⊆ 21 we can find x ∈ 21 such that the set A ∪ (A + x) cannot be covered by any translation of the set B.

Let θ be a nondegenerate skew symmetric real d × d matrix, and let Aθ be the corresponding simple higher dimensional noncommutative torus. Suppose that d is odd, or that d ≥ 4 and the entries of θ are not contained in a quadratic extension of Q. Then Aθ is isomorphic to the transformation group C*-algebra obtained from a minimal homeomorphism of a compact connected one dimensional space locally...

A probability measure in R is called a spectral measure if it has an orthonormal basis consisting of exponentials. In this paper we study spectral Cantor measures. We establish a large class of such measures, and give a necessary and sufficient condition on the spectrum of a spectral Cantor measure. These results extend the studies by Jorgensen and Pedersen [9] and Strichartz [20].

Analysis is the science of measure and optimization. As a collection of mathematical fields, it contains real and complex analysis, functional analysis, harmonic analysis and calculus of variations. Analysis has relations to calculus, geometry, topology, probability theory and dynamics. We will focus mostly on ”the geometry of fractals” today. Examples are Julia sets which belong to the subfiel...

We determine the constructive dimension of points in random translates of the Cantor set. The Cantor set “cancels randomness” in the sense that some of its members, when added to Martin-Löf random reals, identify a point with lower constructive dimension than the random itself. In particular, we find the Hausdorff dimension of the set of points in a Cantor set translate with a given constructiv...

O artigo analisa o álbum “Agropoc”, do cantor e compositor Gabeu. A pesquisa ancorou-se em teorias pós-identitárias como a teoria queer, além da análise musical, visual entrevista com cantor. Conclui-se pela importância para quebra de valores heteronormativos na música sertaneja brasileira.
 PALAVRAS-CHAVE: Música Sertaneja. Teoria Queer. Pocnejo.

A subset E of the d-dimensional torus Td is called a set of uniqueness, or U -set, if every multiple trigonometric series spherically converging to 0 outside E vanishes identically. We show that all countable sets are U -sets and also that HJ sets are U -sets for every J . In particular, C × Td−1, where C is the Cantor set, is an H1 set and hence a U -set. We will say that E is a UA-set if ever...

A metric space (X, d) is monotone if there is a linear order < on X and a constant c such that d(x, y) 6 c d(x, z) for all x < y < z in X. We investigate cardinal invariants of the σ-ideal Mon generated by monotone subsets of the plane. Since there is a strong connection between monotone sets in the plane and porous subsets of the line, plane and the Cantor set, cardinal invariants of these ide...

The Hausdorff–Alexandroff Theorem states that any compact metric space is the continuous image of Cantor’s ternary set C. It is well known that there are compact Hausdorff spaces of cardinality equal to that of C that are not continuous images of Cantor’s ternary set. On the other hand, every compact countably infinite Hausdorff space is a continuous image of C. Here we present a compact counta...