## Hausdorff Measure

Let be a Metric Space, be a Subset of , and a number . The -dimensional Hausdorff measure of , , is the Infimum of Positive numbers such that for every , can be covered by a countable family of closed sets, each of diameter less than , such that the sum of the th Powers of their diameters is less than . Note that may be infinite, and need not be an Integer.

References

Federer, H. Geometric Measure Theory. New York: Springer-Verlag, 1969.

Ott, E. Chaos in Dynamical Systems. Cambridge, England: Cambridge University Press, p. 103, 1993.