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

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

Data and Resources

Additional Info

Field Value
Source https://hal.science/hal-00678595
Author Bayart, Frédéric
Maintainer CCSD
Last Updated May 24, 2026, 23:29 (UTC)
Created May 24, 2026, 23:29 (UTC)
Identifier hal-00678595
Language en
Rights https://about.hal.science/hal-authorisation-v1/
contributor Laboratoire de Mathématiques Blaise Pascal (LMBP) ; Université Blaise Pascal - Clermont-Ferrand 2 (UBP)-Centre National de la Recherche Scientifique (CNRS)
creator Bayart, Frédéric
date 2012-03-13T00:00:00
harvest_object_id 338e98c8-9b20-4f70-9293-4488e1c772a3
harvest_source_id 3374d638-d20b-4672-ba96-a23232d55657
harvest_source_title test moissonnage SELUNE
metadata_modified 2024-04-30T00:00:00
relation info:eu-repo/semantics/altIdentifier/arxiv/1203.2813
set_spec type:UNDEFINED