  This note is a supplement to our paper `Proof of spherical flocking based on
quantitative rearrangement inequalities'. Recently, M. Christ has derived a
deep result concerning stability of the Riesz rearrangement inequality. We are
interested in the special case of this inequality where two of the sets are
equal and the third set is a fixed ball. We show that in this special case,
Christ's proof extends with only minor changes to the case where characteristic
functions are replaced by functions taking values between zero and one.
