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Reference.org
Volterra's function
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<p>In <a href="/facts/Mathematics/pxTouaz4">mathematics</a>, Volterra's function, named for <a href="/facts/Vito_Volterra/gPLlcRu9">Vito Volterra</a>, is a <a href="/facts/Real-valued_function/jetqlJpK">real-valued function</a> <i>V</i> <a href="/facts/Function_of_a_real_variable/bbNG3DnN">defined on the real line</a> R with the following curious combination of properties: </p> <ul><li><i>V</i> is <a href="/facts/Differentiable_function/jQqTgLk1">differentiable</a> everywhere</li> <li>The derivative <i>V</i> ′ is <a href="/facts/Bounded_function/whVjbtuk">bounded</a> everywhere</li> <li>The derivative is not <a href="/facts/Riemann_integration/vWGrPhVh">Riemann-integrable</a>.</li></ul>