  The theory of (Muckenhoupt) weights arises in many areas of analysis, for
example in connection with bounds for singular integrals and maximal functions
on weighted spaces. We prove that a certain averaging process gives a method
for constructing A_p weights from a measurably varying family of dyadic A_p
weights. This averaging process is suggested by the relationship between the
A_p weight class and the space of functions of bounded mean oscillation. The
same averaging process also constructs weights satisfying reverse Holder (RH_p)
conditions from families of dyadic RH_p weights, and extends to the polydisc as
well.
