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.
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 ![[t_0,t_0+l(epsilon)]](/images/equations/AlmostPeriodicFunction/Inline8.svg)
contains at least one number 
for which
![rho[x(t),x(t+tau)]<epsilon](/images/equations/AlmostPeriodicFunction/NumberedEquation1.svg)
.
Another formal description can be found in Krasnosel'skii et al. (1973).
