Let the set
.
A
-cover of F is a countable
or finite union of non-empty subsets
with diameter
less than
which cover F:

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

and
if
.
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
LaTeX2HTML translator Version 97.1 (release) (July 13th,
1997)
Copyright © 1993, 1994, 1995, 1996, 1997,
Nikos Drakos,
Computer Based Learning Unit, University of Leeds.
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
12/17/1997