How behave the typical L^q-dimensions of measures?

2012/03/13 by Frédéric Bayart, Bayart, Frédéric · 1 citation
Mathematics · #Advanced Topology and Set Theory #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematical Analysis and Transform Methods #Mathematical Dynamics and Fractals #math.CA

paper · pdf · doi:10.48550/arxiv.1203.2813

arxiv created 2012/03/13 · openalex publication_date 2012/03/13 · arxiv updated 2012/03/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We compute, for a compact set K⊂\mathbb R^d, the value of the upper and of the lower L^q-dimension of a typical probability measure with support contained in K, for any q∈\mathbb R. Different definitions of the "dimension" of K are involved to compute these values, following q∈\mathbb R.

Cited by

• Some remarks on the exponential separation and dimension preserving approximation for sets and measures

Related

• On measures that improve L^q dimension under convolution
• Measures with specified support and arbitrary Assouad dimensions
• Some remarks on the exponential separation and dimension preserving approximation for sets and measures
• The Quantization Dimension of Distributions
• Intermediate dimensions of measures: Interpolating between Hausdorff and Minkowski dimensions