Approximation in different smoothness spaces with the RAFU method

[EN] The RAFU method is an original and unknown approximation procedure we can use in Approximation Theory. We know that the RAFU method provides a linear space uniformly dense in C[a,b] by using some separation conditions. In this work, we will show we can employ the RAFU method to approximate functions of C0(R) and C00(R), Riemann integrable functions, Lebesgue integrable functions, functions of Lp[a,b] and Lp(R), 1≤p<¥ and measurable functions. Moreover, Riemann integrals can be approximated by the integrals of the functions that the RAFU method provides.