Volterra's function
In mathematics, Volterra's function, named for Vito Volterra, is a real-valued function V defined on the real line R with the following curious combination of properties: V is differentiable everywhere The derivative V ′ is bounded everywhere The derivative is not Riemann-integrable. == Definition and construction == The function is defined by making use of the Smith–Volterra–Cantor set and an infinite number or "copies" of sections of the function defined by f ( x ) = { x 2 sin ( 1 / x ) , x ≠ 0 0 , x = 0.