Uniform Distributions on the Integers: A connection to the Bernouilli Random Walk

Joseph B. Kadane and Jiashun Jin

Econometric Reviews, 2014, vol. 33, issue 1-4, 372-378

Abstract: Associate to each subset of the integers its almost sure limiting relative frequency under the Bernouilli random walk, if it has one. The resulting probability space is purely finitely additive, and uniform in the sense of residue classes and shift-invariance. However, it is not uniform in the sense of limiting relative frequency.

Date: 2014
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DOI: 10.1080/07474938.2013.807193

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