We generalize an important property of trigonometric series to the case of series by orthonormal spline systems corresponding to the dyadic sequence of grid points. We prove that Ciesielski series cannot diverge to infinity on a set of positive measure.

中文翻译：

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正交样条级数收敛到无穷大

我们将三角级数的一个重要性质推广到对应于网格点的二进序列的正交样条系统的级数情况。我们证明 Ciesielski 级数在一组正测度上不能发散到无穷大。