Bartle–Dunford–Schwartz integral

Summary

The Bartle–Dunford–Schwartz integral integrates a scalar function against a countably additive vector measure with values in a Banach space. The integral of a function is then a vector of the Banach space. It is built from simple functions, as the Lebesgue integral is. It is a standard tool for spectral measures and for operators on spaces of continuous functions.