Prime Residue Class of Uniform Charges on the Integers

Michael Spece () and Joseph B. Kadane ()
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Michael Spece: Carnegie Mellon University
Joseph B. Kadane: Carnegie Mellon University

Journal of Theoretical Probability, 2020, vol. 33, issue 1, 340-360

Abstract: Abstract There is a probability charge on the power set of the integers that gives probability 1 / p to every residue class modulo a prime p. There exists such a charge that gives probability w to the set of prime numbers iff $$w \in [0,1/2]$$w∈[0,1/2]. Similarly, there is such a charge that gives probability x to a residue class modulo c, where c is composite, iff $$x \in [0,1/y]$$x∈[0,1/y], where y is the largest prime factor of c.

Keywords: Probability charge; Finite additivity; Uniform distribution; Residue class; Prime numbers; 60A05 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s10959-018-0860-y

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