  In this note we prove that almost cap sets $A \subset \mathbb{F}_q^n$, i.e.,
the subsets of $\mathbb{F}_q^n$ that do not contain too many arithmetic
progressions of length three, satisfy that $|A| < c_q^n$ for some $c_q < q$. As
a corollary we prove a multivariable analogue of Ellenberg-Gijswijt theorem.
