The Uniform Distribution and Benford's Law

The uniform distribution characterization of Benford's law is the most basic and powerful of all characterizations, largely because the mathematical theory of uniform distribution modulo one is very well developed for authoritative surveys. This chapter records and develops tools from that theory which will be used throughout this book to establish Benford behavior of sequences, functions, and random variables. Topics discussed include uniform distribution characterization of Benford's law, uniform distribution of sequences and functions, and uniform distribution of random variables.