2021/06/28 by Jonathan M. Keith, Keith, Jonathan M., Greg Markowsky +1
Computer Science · Mathematics · #28A12 #28C99 #Benford’s Law and Fraud Detection #Computability, Logic, AI Algorithms #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Dynamics and Fractals
paper · pdf · doi:10.48550/arxiv.2107.01020
openalex publication_date 2021/06/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The Cesàro limit - the asymptotic average of a sequence of real numbers - is an operator of fundamental importance in probability, statistics and mathematical analysis. To better understand sequences with Cesàro limits, this paper considers the space F comprised of all binary sequences with a Cesàro limit, and the associated functional ν: F → [0,1] mapping each such sequence to its Cesàro limit. The basic properties of F and ν are enumerated, and chains (totally ordered sets) in F on which ν is countably additive are studied in detail. The main result of the paper concerns a structural property of the pair (F,ν), specifically that F can be factored (in a certain sense) to produce a monotone class on which ν is countably additive. In the process, a slight generalisation and clarification of the monotone class theorem for Boolean algebras is proved.