# Scaling Law of the Hausdorff Measure

• Accepted : 2009.06.03
• Published : 2009.12.31
• 24 10

#### Abstract

We exhibit an example that the scaling property of Hausdorff measure on $\mathbb{R}^{\infty}$ does not hold.

#### Keywords

scaling property;Hausdorff measure

#### References

1. N. Castro and M. Reyes, Hausdorff measures and dimension on $\mathbb{R}^{\infty}$, Proceed. of Amer. Math. Soc., 125(1997), 3267-3273. https://doi.org/10.1090/S0002-9939-97-03944-0
2. M. Csornyei and R. D. Mauldin, Scaling properties of Hausdorff and packing measures, Math. Ann., 319(2001), 817-836. https://doi.org/10.1007/PL00004461
3. K. Falconer, Fractal Geometry:Mathematical Foundations and Applications, John Wiley and Sons (1990).
4. R. D. Mauldin and S. C. Williams, Scaling Hausdorff measures, Mathematika, 36(1989), 325-333. https://doi.org/10.1112/S0025579300013164