Uniform Measure and Uniform Dimension Results for the Image of Subset under Processes with Stable Components

LetX（t）=(X₁（t）,…,X_N（t）) be a d-dimensional process, where X_i（t） is a α_i,-order stable d_i-dimensional process. Assume 0<α_n<…<α₁≤2,d=d₁+…+d_N. In this paper, when α₁ ≤ d₁, we obtain the uniform bounds on the Hausdorff and packing measure of the image X（E） of a Borel set E under a process X（t） with stable components. When α₁ ＞ d₁, the uniform upper is obtained. Uniform dimension theorem is given.