  We consider the multiple products of relevant and marginal scalar composite
operators at the Gaussian fixed-point in $D=4$ dimensions. This amounts to
perturbative construction of the $\phi^4$ theory where the parameters of the
theory are momentum dependent sources. Using the exact renormalization group
(ERG) formalism, we show how the scaling properties of the sources are given by
the short-distance singularities of the multiple products.
