Integrability

Integrability is a mathematical concept used in different areas. It can refer to:

A property of functions or sets depending on a measure. There are p-integrable functions for any positive real number p. See Lp space.
A property of modules of differential forms, which relates to foliations and the Frobenius theorem. See integrability conditions for differential systems.
The integrability of an ordinary differential equation may refer to integration by quadratures (indefinite integrals); or to the existence of enough integrals of the system.
In physics, integrable models