  A histogram estimate of the Radon-Nikodym derivative of a probability measure
with respect to a dominating measure is developed for binary sequences in
$\{0,1\}^{\mathbb{N}}$. A necessary and sufficient condition for the
consistency of the estimate in the mean-square sense is given. It is noted that
the product topology on $\{0,1\}^{\mathbb{N}}$ and the corresponding dominating
product measure pose considerable restrictions on the rate of sampling required
for the requisite convergence.
