It is well known that the space of invariant probability measures for transitive sub-shifts of finite type is a Poulsen simplex. In this article we prove that in the non-compact setting, for a large family of transitive countable Markov shifts, the space of invariant sub-probability measures is a Poulsen simplex and that its extreme points are the ergodic invariant probability measures together with the zero measure. In particular, we obtain that the space of invariant probability measures is a Poulsen simplex minus a vertex and the corresponding convex combinations. Our results apply to finite entropy non-locally compact transitive countable Markov shifts and to every locally compact transitive countable Markov shift. In order to prove these results we introduce a topology on the space of measures that generalizes the vague topology to a class of non-locally compact spaces, the topology of convergence on cylinders. We also prove analogous results for suspension flows defined over countable Markov shifts.

众所周知，有限类型的传递子移位的不变概率测度空间是 Poulsen 单纯形。在本文中，我们证明了在非紧致设置中，对于一大群可传递的可数马尔可夫位移，不变子概率测度的空间是 Poulsen 单纯形，其极值点是遍历不变概率测度和零措施。特别地，我们得到不变概率测度的空间是一个 Poulsen 单纯形减去一个顶点和相应的凸组合。我们的结果适用于有限熵非局部紧凑传递可数马尔可夫移位和每个局部紧凑传递可数马尔可夫移位。为了证明这些结果，我们在度量空间上引入了一个拓扑，将模糊拓扑推广到一类非局部紧凑空间，圆柱上的收敛拓扑。我们还证明了在可数马尔可夫位移上定义的悬浮流的类似结果。