  We show that the algebra of asymptotic functions $^\rho\mathcal{E}(\Omega)$
(introduced in another paper by the author of this article jointly with M.
Oberguggenberger) is isomorphic to a class of pointwise functions in the field
of A. Robinson asymptotic numbers $^\rho\mathbb{C}$. Since the algebra
$^\rho\mathcal{E}(\Omega)$, contains a copy of the Schwartz distributions
$\mathcal{D}^\prime(\Omega)$, it follows that every Schwartz distribution is a
pointwise function in the field $^\rho\mathbb{C}$. The class of asymptotic
functions $^\rho\mathcal{E}(\Omega)$ is an algebra of generalized functions of
Colombeau's type. The field of the constants of this algebra (the functions
with zero gradient) coincides with Robinson field $^\rho\mathbb{C}$.The
expected applications are to PDE with variable, possibly discontinuous,
coefficients and non-linear PDE with singularities.
