本篇論文研究矩陣值勢能在sofic shift 空間上相對應的平衡測度。用本篇論文所造出來的平衡測度，可以得到在sofic shift 空間上維度的譜分析的結果。最重要的是，我們提供一個在sofic shift 空間上，測度$ u$是嚴格的sofic 測度的例子。 This thesis studies equilibrium measures that correspond to the matrix-valued potential on a sofic shift space. With the construction, the analysis of dimension spectrum is then available. Most important of all, there is an example shows that $ u$ is a strict sofic measure.
