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A Rough Differentiable Function
A real-valued continuously differentiable function f on the unit interval is constructed such that ∞ ∑ k=1 βf (x, 2 −k) = ∞ holds for every x ∈ [0, 1]. Here βf (x, 2−k) measures the distance of f to the best approximating linear function at scale 2−k around x.
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1916
ISSN: 0002-9947
DOI: 10.1090/s0002-9947-1916-1501044-1