Work

Pointwise Lower Dimension of Some Quasi-Bernoulli Measures and the Exact-dimensionality Property

Year: 2025

Type: article

Abstract: The main purpose of this paper is to study the pointwise lower dimension of a measure, as a natural dual to the notion of pointwise Assouad dimension introduced by Anttila (2023), by a number of examples. This concept describes the extreme local behavior of a measure around a given point. We verify the exact dimensionality property for quasi-Bernoulli measures supported on self-conformal sets satisfying the strong separation condition. In particular, we compute the pointwise lower dimension explicitly for invariant measures with place-dependent probabilities on self-conformal sets, self-similar doubling measures satisfying the open set condition, and self-affine measures on Bedford–McMullen sponges satisfying the very strong separation condition, which complement the results by Anttila (2023).

Source: Taiwanese Journal of Mathematics

DOI: 10.11650/tjm/250808

Author: Qiang Huo

Institution: University of Science and Technology of China

Language: English

Topic: Mathematical Dynamics and Fractals

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funders: National Natural Science Foundation of China, China Postdoctoral Science Foundation

Awards: G2645454641, G3701778458