Geodesic
Hausdorff and packing measure for thick solenoids
Michał Rams 1
1 Institute of Mathematics Polish Academy of Sciences P.O. Box 21 00-956 Warszawa, Poland and Université de Bourgogne Dijon, France
Studia Mathematica, Tome 163 (2004) no. 2, pp. 193-202 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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For a linear solenoid with two different contraction coefficients and box dimension greater than 2, we give precise formulas for the Hausdorff and packing dimensions. We prove that the packing measure is infinite and give a condition necessary and sufficient for the Hausdorff measure to be positive, finite and equivalent to the SBR measure. We also give analogous results, generalizing [P], for affine IFS in $\mathbb R^2$.
DOI : 10.4064/sm163-2-7
Keywords: linear solenoid different contraction coefficients box dimension greater nbsp precise formulas hausdorff packing dimensions prove packing measure infinite condition necessary sufficient hausdorff measure positive finite equivalent sbr measure analogous results generalizing affine ifs mathbb

Michał Rams  1

1 Institute of Mathematics Polish Academy of Sciences P.O. Box 21 00-956 Warszawa, Poland and Université de Bourgogne Dijon, France 
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Michał Rams. Hausdorff and packing measure for thick solenoids. Studia Mathematica, Tome 163 (2004) no. 2, pp. 193-202. doi: 10.4064/sm163-2-7

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