Given a separated dual system (E, E'), the Fenchel transform determines a pairing of the convex functions on E with the convex functions on E'. This operation is shown to have a continuity property.

A necessary and sufficient condition is obtained for an L function to have a continuous derivative of the kth order. Other results concerning the continuity properties of infinitely divisible ...

The original version of this story appeared in Quanta Magazine. Calculus is a powerful mathematical tool. But for hundreds of years after its invention in the 17th century, it stood on a shaky ...