| Abstract: |
| In this talk, we discuss several types of low complexity of finite partitions in a standard probability space, including precompactness, zero maximal pattern entropy, bounded mean complexity and mean equicontinuity. We show that a collection of finite partitions is precompactness in the Rokhlin metric if and only if it has zero maximal pattern entropy if and only if the collection of the characteristic functions of atoms in the partitions is precompactness in $L^2$ if and only if it has bounded mean complexity with respect the Hamming distance. Then we apply this result to the complexity of a partition of countably infinite discrete amenable group actions. This talk is based on a joint work with Tao Yu and Xianliang Zhong. |
|