  We present a general construction of non-Gaussian probability measures on the
space of distributional kernels obeying a natural extension of the
Osterwalder-Schrader axioms of Euclidean quantum field theory in arbitrary
space-time dimension $d$. These measures may be interpreted as corresponding to
scalar massive quantum fields with polynomial self-interaction. As a
consequence, we obtain examples of non-free models satisfying the Haag-Kastler
axioms of algebraic quantum field theory for arbitrary $d$. When $d<4$ we are
able to transfer the measures to the space of distributions and verify the
standard Osterwalder-Schrader axioms, hence, by a well-known reconstruction
theorem, we also obtain quantum field theory models satisfying the axioms of
Wightman.
