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Local conical dimensions for measures

Published online by Cambridge University Press:  07 February 2013

DE–JUN FENG ,
ANTTI KÄENMÄKI  and
VILLE SUOMALA
DE–JUN FENG
Affiliation:
The Chinese University of Hong Kong, Shatin, Hong Kong. e-mail: djfeng@math.cuhk.edu.hk
ANTTI KÄENMÄKI
Affiliation:
Department of Mathematics and Statistics, P.O. Box 35 (MaD), FI-40014 University of Jyväskylä, Finland. e-mail: antti.kaenmaki@jyu.fi
VILLE SUOMALA
Affiliation:
Department of Mathematical Sciences, P.O. Box 3000, FI-90014 University of Oulu, Finland. e-mail: ville.suomala@oulu.fi
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Abstract

We study the decay of μ(B(x,r)∩C)/μ(B(x,r)) as r ↓ 0 for different kinds of measures μ on ℝn and various cones C around x. As an application, we provide sufficient conditions that imply that the local dimensions can be calculated via cones almost everywhere.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 154 , Issue 3 , May 2013 , pp. 465 - 479
Copyright
Copyright © Cambridge Philosophical Society 2013

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