Tail sums of Takagi class functions obey LLN, CLT and LIL exactly when the coefficient sequence decays slowly, while geometric decay gives a nonconstant limit in distribution.
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On the rate of convergence for Takagi class functions
Tail sums of Takagi class functions obey LLN, CLT and LIL exactly when the coefficient sequence decays slowly, while geometric decay gives a nonconstant limit in distribution.