  Constrained quantization for a Borel probability measure refers to the idea
of estimating a given probability by a discrete probability with a finite
number of supporting points lying on a specific set. The specific set is known
as the constraint of the constrained quantization. A quantization without a
constraint is known as an unconstrained quantization, which traditionally in
the literature is known as quantization. Constrained quantization has recently
been introduced by Pandey and Roychowdhury. In this paper, for a uniform
distribution with support lying on a side of an equilateral triangle, and the
constraint as the union of the other two sides, we obtain the optimal sets of
$n$-points and the $n$th constrained quantization errors for all positive
integers $n$. We also calculate the constrained quantization dimension and the
constrained quantization coefficient.

Probability