We introduce a generalization of the Takagi Class, considering an arbitrary countable dense set instead of the dyadic numbers that appear in the original Takagi function. This generalization contains many of the previous generalizations. We study the differentiation of the functions belonging to this Class, as well as the measure of the set of points of differentiability characterizing them through properties of the weights sequence. Finally, we prove that the Class is a Banach space isometric to \(\ell ^1\).

中文翻译：

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广义高木类功能的可微性

我们引入Takagi类的泛化，考虑了任意可数的密集集，而不是出现在原始Takagi函数中的二进数字。此概括包含许多以前的概括。我们研究了属于该类的函数的微分，以及通过权重序列的性质来表征它们的可微分点集的度量。最后，我们证明该类是与\（\ ell ^ 1 \）等距的Banach空间。