Journal of the Mathematical Society of Japan

A note on the dimensions of Assouad and Aikawa


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We show that in Euclidean space and other regular metric spaces, the notions of dimensions defined by Assouad and Aikawa coincide. In addition, in more general metric spaces, we study the relationship between these two dimensions and a related codimension and give an application of the Aikawa (co)dimension for the Hardy inequalities.

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J. Math. Soc. Japan, Volume 65, Number 2 (2013), 343-356.

First available in Project Euclid: 25 April 2013

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Zentralblatt MATH identifier

Primary: 54F45: Dimension theory [See also 55M10]
Secondary: 28A12: Contents, measures, outer measures, capacities 54E35: Metric spaces, metrizability 26D15: Inequalities for sums, series and integrals

Assouad dimension Aikawa dimension metric space doubling measure Hardy inequality


LEHRBÄCK, Juha; TUOMINEN, Heli. A note on the dimensions of Assouad and Aikawa. J. Math. Soc. Japan 65 (2013), no. 2, 343--356. doi:10.2969/jmsj/06520343.

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