We consider a generalized version of the Takagi function, which is one of the most famous example of nowhere differentiable continuous functions. We investigate a set of conditions to describe the rate of convergence of Takagi class functions from the probabilistic point of view: The law of large numbers, the central limit theorem, and the law of the iterated logarithm. On the other hand, we show that the Takagi function itself does not satisfy the law of large numbers in the usual sense.

中文翻译：

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关于 Takagi 类函数的收敛速度

我们考虑高木函数的广义版本，它是无处可微连续函数最著名的例子之一。我们从概率的角度研究了一组条件来描述高木类函数的收敛速度：大数定律、中心极限定理和迭代对数定律。另一方面，我们证明了高木函数本身并不满足通常意义上的大数定律。