测度空间的拓扑序列熵

给定一个拓扑动力系统（X，T），记M（X）为X上Borel概率测度的全体，其上的拓扑由弱拓扑所诱导．如果系统（X，T）具有零拓扑序列熵，则它称为拓扑-null的．对于给定的一个伪度量空间以及其上的一个自映射（不必连续），引入并研究沿着给定序列的拓扑熵，包括由空间上连续实值函数所诱导的伪度量．作为应用可以证明，给定一个序列A包含于Z＋，如果X为零维的，那么，系统（X，T）沿着A具有零拓扑熵当且仅当（M（X），T）沿着A具有零拓扑熵．特别的，当X为一个零维空间时，系统（X，T）为拓扑-null的当且仅当（M（X），T）为拓扑-null的．

Topological sequence entropy of the space of measures

Let (X, T) be a TDS and M(X) the space of all Borel probability measures on X equipped with the weak* topology. (X, T) is topo-null if (X, T) has zero topological sequence entropy. Given a pseudo-metric space and a self-map, the topological sequence entropy was studied for a special class of pseudo-metrics induced by continuous real-valued functions on the space. As an application, it was proved that, given a sequence A(∈)Z+, if X is zero-dimensional then (X, T) has zero topological entropy along A if and only if (M (X), T) has zero topological entropy along A. In particular, if X is zero-dimensional then (X,T) is topo-null if and only if (M (X), T) is topo-null.