The spatial homogeneity is an important character for Levy-processes on Eu-clidean space Rｄ.The analogy for the Measure-valued branchinng processes over LevyProcesses (also called Super-Levy processes) will be discussed in this paper. That is thetranslation-invariaut in the sense of distributions. Moreover some stronger results arealso derived for the special Measure-valued branching processes when their initial mea-sures are given by the Lebesguc measure.
