A function representable as a generalized Fourier series. Let be a metric space with metric
.
Following Bohr (1947), a continuous function
for
with values in
is called an almost periodic function if, for every , there exists such that every interval contains at least one number for which
for .
Another formal description can be found in Krasnosel'skii et al. (1973).
Every almost periodic function is bounded and uniformly continuous on the entire
real line.