11. :: : This would almost be the class of Henstock-Kurzweil Integrable functions . 12. This transform continues to enjoy many of the properties of the Fourier transform of integrable functions . 13. For any integrable function and all set 14. In effect, this makes it possible to speak of Fourier transforms of quadratically integrable functions . 15. To afford a unitary representation of " G " on square-integrable functions . 16. The Hardy Littlewood maximal inequality states that for an integrable function " f ", 17. These results remain true for the Henstock Kurzweil integral, which allows a larger class of integrable functions . 18. Linearity : If and are Lebesgue integrable functions and and are real numbers, then is Lebesgue integrable and 19. This space is isomorphic to the space of Lebesgue integrable functions modulo the subspace of functions with integral zero. 20. And found close connections between cube tilings and the spectral theory of square-integrable functions on the cube.
