Bohr almost periodic function

Summary

A Bohr almost periodic function is a continuous function on the real line whose $\varepsilon$-almost periods are spread evenly over the line, for every $\varepsilon > 0$. This was Harald Bohr's original definition of an almost periodic function. These functions are exactly the uniform limits of trigonometric polynomials with arbitrary real frequencies, by Bohr's approximation theorem. They have a mean value and a Fourier series, and they form a closed subalgebra of the bounded continuous functions.