Mathematical Proceedings of the Cambridge Philosophical Society

Research Article

Fractal properties of products and projections of measures in xs211Dd

Xiaoyu Hua1 and S. James Taylora1

a1 Department of Mathematics, University of Virginia, Charlottesville, VA 22903, U.S.A.

Abstract

Borel measures in xs211Dd are called fractal if locally at a.e. point their Hausdorff and packing dimensions are identical. It is shown that the product of two fractal measures is fractal and almost all projections of a fractal measure into a lower dimensional subspace are fractal. The results rely on corresponding properties of Borel subsets of xs211Dd which we summarize and develop.

(Received May 17 1993)

(Revised September 20 1993)

Footnotes

† Some of the results in this paper were first obtained and presented as part of the Ph.D. dissertation at the University of Virginia of this author (1992).

‡ Research partially supported by NSF Contract 9001401.