Fomenko is the author of the theory of topological invariants of an integrable Hamiltonian system. Such systems of integrable differential equations are called integrable systems. But it may happen that improper integrals exist for functions that are not Lebesgue integrable. The convolution defines a product on the linear space of integrable functions. This includes the case of improperly Riemann integrable functions. In effect, this makes it possible to speak of Fourier transforms of quadratically integrable functions. There is also a notion of quantum integrable systems. In particular, any locally integrable function has a distributional derivative. The converse does not hold, as the (integrable, but discontinuous) sign function shows. One particularly important class of Radon measures are those that are induced locally integrable functions. The test functions are themselves locally integrable, and so define distributions. Suppose is an integrable and square-integrable function. There is no guarantee that every function is Lebesgue integrable. Then the function is also integrable on . Suppose that formula 242 and each f is integrable on E.