For many dynamical systems that are popular in applications, estimates are known for the decay of large deviations of the ergodic averages in the case of Hölder continuous averaging functions. In the present article, we show that these estimates are valid with the same asymptotics in the case of bounded almost everywhere continuous functions. Using this fact, we obtain, in the case of such functions, estimates for the rate of convergence in Birkhoff’s ergodic theorem and for the distribution of the time of return to a subset of the phase space.

中文翻译：

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遍历平均数的较大偏差：从Hölder连续性到几乎所有地方的连续性

对于许多在应用中流行的动力学系统，在Hölder连续平均函数的情况下，估算出的遍历平均值的大偏差会衰减。在本文中，我们证明了在几乎无处不在的连续函数有界的情况下，这些估计对于相同的渐近性是有效的。利用这一事实，在这种函数的情况下，我们获得了伯克霍夫遍历定理中收敛速度的估计以及返回到相空间子集的时间分布的估计。