ON THE SPACE OF ERGODIC INVARIANT-MEASURES OF UNIPOTENT FLOWS
ON THE SPACE OF ERGODIC INVARIANT-MEASURES OF UNIPOTENT FLOWS
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DOI：
10.1017/s0143385700008282
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发表时间：
1995-02-01
影响因子：
0.9
通讯作者：
SHAH, N
中科院分区：
文献类型：
--
作者：
MOZES, S;SHAH, N
设 G 为李群，Gamma 为离散子群。我们证明，如果 {mu(n)} 是 G/Gamma 上的概率测度的收敛序列，并且在单能单参数子群的作用下是不变且遍历的，那么这样一个序列的极限 mu 在保存它的子群的闭轨道上得到支持，并且对于 G 的单能单参数子群的作用是不变和遍历的。
Let G be a Lie group and Gamma be a discrete subgroup. We show that if {mu(n)} is a convergent sequence of probability measures on G/Gamma which are invariant and ergodic under actions of unipotent one-parameter subgroups, then the limit mu of such a sequence is supported on a closed orbit of the subgroup preserving it, and is invariant and ergodic for the action of a unipotent one-parameter subgroup of G.