Research Article

Rings of fractional dimension

K. J. Falconera1

a1 School of Mathematics, University Walk, Bristol. BS8 1TW

We define s-dimensional Hausdorff outer measure on subsets of n by


Here | | denotes the diameter of a set. The Souslin sets, which include the Borel sets, are Hs-measurable for any s ≥ 0.

(Received December 05 1983)

Key Words:

  • 28A75: MEASURE AND INTEGRATION; Classical measure theory; Other geometric measure theory