Weakly measurable function

In mathematics—specifically, in functional analysis—a weakly measurable function taking values in a Banach space is a function whose composition with any element of the dual space is a measurable function in the usual (strong) sense. For separable spaces, the notions of weak and strong measurability agree.

The relationship between measurability and weak measurability is given by the following result, known as Pettis' theorem or Pettis measurability theorem.