  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 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.
