Bochner integral

Summary

The Bochner integral extends the Lebesgue integral to functions with values in a Banach space. It is defined as a limit of integrals of simple functions, approximated in the mean. A strongly measurable function is Bochner integrable exactly when the integral of its norm is finite. It keeps the main theorems of Lebesgue integration, such as dominated convergence. It is the standard integral for vector-valued functions in analysis and partial differential equations.