Quantization for uniform distributions on stretched Sierpi\'nski triangles

Abstract

In this paper, we have considered a uniform probability distribution supported by a stretched Sierpi\'nski triangle. For this probability measure, the optimal sets of $n$-means and the $n$th quantization errors are determined for all $n\geq 2$. In addition, it is shown that the quantization coefficient for such a measure does not exist though the quantization dimension exists.