almost periodic function (equivalent definition)

There is an equivalent definition of almost periodic function due to Bochner:

A function $f\colon\mathbb{R}\to\mathbb{R}$ is almost periodic if every sequence of translates of $f$ has a uniformly convergent subsequence.

Not only is this definition simpler to state than that of Bohr, but it also generalizes to functions on groups.

Title almost periodic function (equivalent definition) AlmostPeriodicFunctionequivalentDefinition 2013-03-22 15:23:03 2013-03-22 15:23:03 rspuzio (6075) rspuzio (6075) 8 rspuzio (6075) Definition msc 42A75