Pettis integral

Summary

The Pettis integral of a function with values in a Banach space is a vector in that space. Each continuous linear functional maps it to the integral of the corresponding scalar function. It is a weak notion of integral, defined through the dual space. Every Bochner integrable function is Pettis integrable with the same integral, but in infinite dimensions there are Pettis integrable functions that are not Bochner integrable. It is also called the Gelfand–Pettis integral.