Hausdorff measures and dimension on ![]() |
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Authors: | Nieves Castro Miguel Reyes |
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Affiliation: | Departamento de Matemática Aplicada, Facultad de Informática, Campus de Montegancedo, Boadilla del Monte, 28660 Madrid, Spain ; Departamento de Matemática Aplicada, Facultad de Informática, Campus de Montegancedo, Boadilla del Monte, 28660 Madrid, Spain |
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Abstract: | We consider the Hausdorff measures , , defined on with the topology induced by the metric ![begin{displaymath}rho (x,y) = sum _{i=1}^{infty } |x_{i}-y_{i}|/2^{i}(1+|x_{i}-y_{i}|),end{displaymath}](http://www.ams.org/proc/1997-125-11/S0002-9939-97-03944-0/gif-abstract/img6.gif)
for all . We study its properties, their relation to the ``Lebesgue measure" defined on by R. Baker in 1991, and the associated Hausdorff dimension. Finally, we give some examples. |
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Keywords: | |
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