. This article presents differentiable characteristics of the Blancmange function on ℝ. The function has singularities of each point on ℝ. The first, it will be proven that function is continuous at each point on ℝ, and then by constructing of an infinite series of the saw tooth function, will be proven that the Blancmange function is differentiable nowhere at each point on ℝ. At the end of this article, also discussed integrable analysis of Blancmange function.
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