CERTAIN INDUCED MEASURES AND THE FRACTIONAL DIMENSIONS OF THEIR ' 'SUPPORTS' ',
Abstract
A direct proof of a slightly generalized version of a theorem of Kakutani concerning product measures is presented. A class of measures on the unit interval is considered as a special case and the fractional (Hausdorff) dimensions of the 'supports' of these measures are calculated. Finally, it is shown how a certain class of absolutely continuous measures can be represented as convolutions of singular measures based on small sets (in the sense of Hausdorff dimension). In particular, the Lebesque measure on the unit interval is demonstrated as a convolution of two singular measures each based on a set of fractional dimension zero. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Nov 01, 1963
- Accession Number
- AD0426493
Entities
People
- S. D. Chatterji
Organizations
- University of Wisconsin–Madison