2006/07/11 by Élliott H. Lieb, Lieb, Elliott H., Daniel N. Osherson +3
Computer Science · Mathematics · #Benford’s Law and Fraud Detection #Computability, Logic, AI Algorithms #Computational Complexity (cs.CC) #FOS: Computer and information sciences #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.cs/0607054
openalex publication_date 2006/07/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Considerable thought has been devoted to an adequate definition of the class of infinite, random binary sequences (the sort of sequence that almost certainly arises from flipping a fair coin indefinitely). The first mathematical exploration of this problem was due to R. Von Mises, and based on his concept of a "selection function." A decisive objection to Von Mises' idea was formulated in a theorem offered by Jean Ville in 1939. It shows that some sequences admitted by Von Mises as "random" in fact manifest a certain kind of systematicity. Ville's proof is challenging, and an alternative approach has appeared only in condensed form. We attempt to provide an expanded version of the latter, alternative argument.