Lower Assouad Dimension of Measures and Regularity

DOI10.1017/S0305004119000458zbMath1479.28010arXiv1812.05573OpenAlexW3105094574MaRDI QIDQ4958690

Sascha Troscheit, Kathryn E. Hare

Publication date: 14 September 2021

Published in: Mathematical Proceedings of the Cambridge Philosophical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1812.05573

zbMATH Keywords

Moran construction\(s\)-regularitylower and upper Assouad dimension

Mathematics Subject Classification ID

Fractals (28A80) Dimension theory of smooth dynamical systems (37C45) Set functions and measures on topological spaces (regularity of measures, etc.) (28C15)

Related Items (10)

Intermediate Assouad-like dimensions ⋮ Minkowski dimension for measures ⋮ INTERMEDIATE ASSOUAD-LIKE DIMENSIONS FOR MEASURES ⋮ Stability and measurability of the modified lower dimension ⋮ Assouad-like dimensions of a class of random Moran measures. II: Non-homogeneous Moran sets ⋮ Intermediate value property for the Assouad dimension of measures ⋮ Interpolating between dimensions ⋮ Almost sure Assouad-like dimensions of complementary sets ⋮ Regularity versus smoothness of measures ⋮ Assouad-like dimensions of a class of random Moran measures

Cites Work

• Quasi-doubling of self-similar measures with overlaps
• A convolution inequality concerning Cantor-Lebesgue measures
• Multifractal decompositions of Moran fractals
• Local dimensions of measures of finite type III -- measures that are not equicontractive
• Measures with predetermined regularity and inhomogeneous self-similar sets
• New dimension spectra: finer information on scaling and homogeneity
• Iterated function systems of finite type and the weak separation property
• Weak separation condition, Assouad dimension, and Furstenberg homogeneity
• HAUSDORFF DIMENSION OF SELF-SIMILAR SETS WITH OVERLAPS
• Uniform perfectness of self-affine sets
• Local Dimensions of Measures of Finite Type II: Measures Without Full Support and With Non-regular Probabilities
• Assouad-type spectra for some fractal families
• The Assouad spectrum and the quasi-Assouad dimension: a tale of two spectra
• On the upper regularity dimensions of measures
• LOWER ASSOUAD-TYPE DIMENSIONS OF UNIFORMLY PERFECT SETS IN DOUBLING METRIC SPACES
• Dimensions, Whitney covers, and tubular neighborhoods
• On Sets of Multiplicity for Trigonometrical Series

This page was built for publication: Lower Assouad Dimension of Measures and Regularity