  A finite word $u$ is called closed if its longest repeated prefix has exactly
two occurrences in $u,$ once as a prefix and once as a suffix. We study the
function $f_x^c:\mathbb N \rightarrow \mathbb N$ which counts the number of
closed factors of each length in an infinite word $x.$ We derive an explicit
formula for $f_x^c$ in case $x$ is an Arnoux-Rauzy word. As a consequence we
prove that $\liminf _{n\rightarrow \infty}f_x^c(n)=+\infty.$
