$n$-digit Benford converges to Benford

TL;DR

This paper proves that as the number of digits increases, an $n$-digit Benford variable converges to a true Benford distribution, based on the sum invariance property.

Contribution

It introduces a proof that $n$-digit Benford variables approach the Benford distribution as $n$ grows large, expanding understanding of digit-based convergence.

Findings

$n$-digit Benford variables converge to Benford distribution

Sum invariance property is key to the proof

Convergence occurs as $n$ approaches infinity

Abstract

Using the sum invariance property of Benford random variables, we prove that an $n$-digit Benford variable converges to a Benford variable as $n$ approaches infinity.