Let \(\nu \) be a Borel probability measure on a d-dimensional Euclidean space \(\mathbb {R}^d\) , \(d\ge 1\) , with a compact support, and let \((p_0, p_1, p_2, \ldots , p_N)\) be a probability vector with \(p_j>0\) for \(0\le j\le N\) . Let \(\{S_j: 1\le j\le N\}\) 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 nth 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.
