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Miklós Schweitzer 1960- Problem 7

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November 21, 2015
college contestsreal analysisFunctional Analysis

Problem Statement

7. Define the generalized derivative at x0x_0 of the function f(x)f(x) by
lim⁡h→021h∫x0x0+hf(t)dt−f(x0)h\lim_{h \to 0} 2 \frac{ \frac{1}{h} \int_{x_0}^{x_0+h} f(t) dt - f(x_0)}{h}
Show that there exists a function, continuous everywhere, which is nowhere differentiable in this general sense ( R. 8)
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