English

Local conical dimensions for measures

Classical Analysis and ODEs 2017-02-03 v1

Abstract

We study the decay of μ(B(x,r)C)/μ(B(x,r))\mu(B(x,r)\cap C)/\mu(B(x,r)) as r0r\downarrow 0 for different kinds of measures μ\mu on Rn\R^n and various cones CC around xx. As an application, we provide sufficient conditions implying that the local dimensions can be calculated via cones almost everywhere.

Keywords

Cite

@article{arxiv.1204.5886,
  title  = {Local conical dimensions for measures},
  author = {De-Jun Feng and Antti Käenmäki and Ville Suomala},
  journal= {arXiv preprint arXiv:1204.5886},
  year   = {2017}
}
R2 v1 2026-06-21T20:55:03.328Z