  We construct an infinite dimensional analysis with respect to non-Gaussian
measures of Mittag-Leffler type which we call Mittag-Leffler measures. It turns
out that the well-known Wick ordered polynomials in Gaussian analysis cannot be
generalized to this non-Gaussian case. Instead of using Wick ordered
polynomials we prove that a system of biorthogonal polynomials, called Appell
system, is applicable to the Mittag-Leffler measures. Therefore we are able to
introduce a test function and a distribution space. As an application we
construct Donsker's delta in a non-Gaussian setting as a weak integral in the
distribution space.
