  Let $\nu$ be a Borel probability measure on a $d$-dimensional Euclidean space
$\mathbb{R}^d$, $d\geq 1$, with a compact support, and let $(p_0, p_1, p_2,
\ldots, p_N)$ be a probability vector with $p_j>0$ for $1\leq j\leq N$. Let
$\{S_j: 1\leq j\leq N\}$ be a set of contractive mappings on $\mathbb R^d$.
Then, a Borel probability measure $\mu$ on $\mathbb R^d$ such that
$\mu=\sum_{j=1}^N p_j\mu\circ S_j^{-1}+p_0\nu$ is called an inhomogeneous
measure, also known as a condensation measure on $\mathbb R^d$. For a given
$r\in (0, +\infty)$, the quantization dimension of order $r$, if it exists,
denoted by $D_r(\mu)$, of a Borel probability measure $\mu$ on $\mathbb R^d$
represents the speed at which the $n$th quantization error of order $r$
approaches to zero as the number of elements $n$ in an optimal set of $n$-means
for $\mu$ tends to infinity. In this paper, we investigate the quantization
dimension for such a condensation measure.
