Let then

If gets smaller the number of allowed covers decreases and the infimum increases and has a limit for :

This limit exists and is called the Hausdorff measure.
If *t*>*s* and
then

So if you explore as a function of *s* there is
a jump from to zero at some *s* which is called the
Hausdorff dimension of *F*.

This document was generated using the

From the sci.fractals FAQ: A clear and concise (2 page) write-up of the definition of the Hausdorff-Besicovitch dimension in MS-Word 6.0 format is available in zip format. hausdorff.zip (~26KB) http://www.newciv.org/jhs/hausdorff.zip

Jürgen Dollinger