  We introduce the space of dyadic bounded mean oscillation functions $f$
defined on $[0,1]^n$ and study the behavior of the nonincreasing rearrangement
of $f$, as an element of the space $BMO((0,1])$. We also study the analogous
class of functions that satisfy the dyadic Gurov-Reshetnyak condition and look
upon their integrability properties.
