An estimation of the Hausdorff measure of the Koch curve. (Chinese. English summary) Zbl 0966.28006

Chen, Erming; Du, Xiufeng

J. Math. Study 32, No. 3, 324-326 (1999).

The following theorem is proved in this note:
Theorem. Let \(K\) be the Koch curve. Then for its Hausdorff measure the estimation \[ H^s(K)< {4^4\over 122} \Biggl[{\sqrt{876}\over 81}\Biggr]^s \] with \(s= \log_34\) holds.

Reviewer: Su Weiyi (Nanjing)

MSC:

28A78	Hausdorff and packing measures
28A80	Fractals

Keywords:

Koch curve; Hausdorff measure