Real analysis

Pompeiu derivative

In mathematical analysis, a Pompeiu derivative is a real-valued function of one real variable that is the derivative of an everywhere differentiable function and that vanishes in a dense set. In particular, a Pompeiu derivative is discontinuous at any point where it is not 0. Whether non-identically zero such functions may exist was a problem that arose in the context of early-1900s research on functional differentiability and integrability. The question was affirmatively answered by Dimitrie Pompeiu by constructing an explicit example; these functions are therefore named after him. (Wikipedia).

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Inverse function | Monotonic function | Linear subspace | Vector space | Homeomorphism | Intersection (set theory) | Differentiable function | Mathematical analysis | Unit interval | Banach space | Rational number | Sequence | Cube root | Bounded function | Dimitrie Pompeiu | Dense set | Function (mathematics) | Surjective function | Weierstrass M-test | Real number | Enumeration algorithm | Linear combination | Baire function | Class (set theory) | Interval (mathematics) | Uniform convergence