AN APPLICATION OF PROHOROV'S THEOREM TO PROBABILISTIC NUMBER THEORY,
Abstract
The pupose of this paper is to give a probabilistic proof of a theorem which contains as special cases certain results about the natural densities of arithmetically interesting sets of integers, results usually conjectured on probabilistic grounds but proved by nonprobabilistic methods. The principle tool is Prohorov's theorem on the weak compactness of probability measures. Results similar to those of this paper, but for logarithmic density rather than natural density, have been proved, by very different methods. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Jan 01, 1963
- Accession Number
- AD0415394
Entities
People
- Patrick Billingsley
Organizations
- University of Chicago