Fleming-Viot测度值随机过程是源自种群遗传模型的取值为概率测度的随机过程。一个大样本数量的生物种群繁衍后代，且繁衍过程中可能出现基因变异、选择和重组。Fleming-Viot测度值随机过程描述这样的种群里不同种类基因相对比例的演变。. 我们的研究集中在测度值随机过程支撑的几何性质和种群遗传模型的溯祖过程。首先，我们讨论Fleming-Viot测度值随机过程支撑的性质，包括确切的Hausdorff维数、Hausdorff测度函数、支撑的扩展速度、超Levy过程支撑的瞬间扩张性质等。其次，我们利用Fleming-Viot测度值随机过程的对偶聚合（coalescent）过程的理论知识，来描述样本数量足够大的双倍体种群遗传模型里关于选定样本基因中所蕴含的祖先基因过程的构造。. 该项研究将丰富测度值随机过程的理论知识，促进数学与生物交叉学科的发展。

The Fleming-Viot measure-valued stochastic process is probability-measure-valued stochastic process arising from population genetic models. It describes the evolution of relative frequencies for different types of alleles in a large population that undergoes resampling together with possible mutation, selection and recombination. ..Our research focus on the geometric property of support for measure-valued stochastic processes and the ancestral process for population genetic models. Firstly, we discuss the support properties of Fleming-Viot measure-valued stochastic process, including the exact Hausdorff dimension, the Hausdorff measure function, the growth rate for the support and the support propagation property for super Levy process etc. Secondly, we apply the theory of dual coalescent process for Fleming-Viot measure-valued stochastic process to describe the classification of the ancestral structure for a sample of genes in diploid population model when the total population size is sufficiently large. ..Our research will enrich the theory of measure-valued stochastic process and promote the development of cross discipline between Mathematics and Biology.