Solution
= Solution
For the counting-measure <Lp norm>, define
$$
\operatorname{AP}_{2m}(f;X)
=\{t\in\mathbb F_p^n:\|\tau_tf-f\|_{2m}\leq X\},
\qquad (\tau_tf)(x)=f(x+t).
$$
This is the set of <Lp almost periods> of $f$ with exponent $p=2m$ and error $X$.