  We investigate some topological properties of a normal functor $H$ introduced
earlier by Radul which is some functorial compactification of the
Hartman--Mycielski construction HM. We prove that the pair ($HX$, HM$Y$) is
homeomorphic to the pair $(Q,\sigma)$ for each nondegenerated metrizable
compactum $X$ and each dense $\sigma$-compact subset $Y$.
