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Article: Using finitely additive probability: uniform distributions on the natural numbers.
- Article from:
- Journal of the American Statistical Association
- Article date:
- June 1, 1995
- Author:
CopyrightCOPYRIGHT 1995 American Statistical Association. This material is published under license from the publisher through the Gale Group, Farmington Hills, Michigan. All inquiries regarding rights should be directed to the Gale Group. (Hide copyright information)
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1. INTRODUCTION
Suppose that a computer scientist asks you for help with finding the probability that a random integer has some property, such as that it can be expressed as the sum of squares of two integers. She says that by "random" she means something akin to a uniform distribution, in the sense that every integer, no matter how large, will have the same probability. How can such a question be answered in terms of modern probability theory?
One might try to represent the "random" integer by a countably additive probability measure [Mu]; that is, one satisfying the condition
[Mathematical Expression Omitted],
where the sets [A.sub.i] are ...