Fuchsian groups and ergodic theory
Fuchsian groups and ergodic theory
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Fuchsian 群和遍历理论
DOI：
10.1090/s0002-9947-1936-1501848-8
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发表时间：
1936
期刊：
影响因子：
--
通讯作者：
E. Hopf
中科院分区：
文献类型：
--
作者：
E. Hopf
严格遍历性比（B）更强更重要。我们假设m（Q）是有限的。(c)设f（P）是Q上的任意m可和函数。因此，沿着运动曲线的时间平均off（P）一般等于fj（P）dm/m（Q），例外曲线形成Q上m测度为零的点集。如果我们以下列方式说明这些概念，就能最清楚地看出它们是如何相互关联的。（a '）Q上的每个在流下不变的开点集在Q上处处稠密。
Still stronger and more important than (b) is strict ergodicity. We suppose m(Q) to be finite. (c) Let f(P) be an arbitrary m-summable function on Q. The time-average off(P) along a curve of motion is then,in general, equal to fj(P)dm/m(Q), the exceptional curves forming a point set on Q of m-measure zero. How these concepts are interrelated is seen most clearly if we state them in the following way. (a') Every open point set on Q that is invariant under the flow is everywhere dense on Q.