🚀 go-pugleaf

In article <ggrzgca@rpi.edu> sassoj@rs6412.ecs.rpi.edu (John J. Sasso Jr.) writes:
>   Now, the Cantor set has Lebesgue measure 0 for the Lebesgue measure defined
>in spaces R^1, R^2, etc...  However, the Cantor does have a fractal dimension
>(or Hausdorff dimension) between 0 and 1 (I cannnot recall the value), and
> log(2)/log(3)

>I'll call this dimension Df.  Is it possible to define a Lebesgue measure in
>a space of dimension Df (R^Df) such that the measure of the Cantor set is a 
>value other than 0?

It sounds like you're looking for Hausdorff measure. See either of Falconer's books:
The Geometry of Fractal Sets, Cambridge University Press, 1985; or
Fractal Geometry, Wiley, 1990.

-John Hart
 School of EECS
 Washington State University
 Pullman, WA 99164-2752