  The exact renormalization group (ERG) is formulated implementing the
decimation of degrees of freedom by means of a particular momentum integration
measure. The definition of this measure involves a distribution that links this
decimation process with the dimensional regularization technique employed in
field theory calculations. Taking the dimension d=4-\epsilon, the one loop
solutions to the ERG equations for the scalar field theory in this scheme are
shown to coincide with the dimensionally regularized perturbative field theory
calculation in the limit \mu\to0, if a particular relation between the scale
parameter \mu and \epsilon is employed. In general, it is shown that in this
scheme the solutions to the ERG equations for the proper functions coincide
when \mu\to0 with the complete diagrammatic contributions appearing in field
theory for these functions and this theory, provided that exact relations
between \mu and \epsilon hold. In addition a non-perturbative approximation is
considered. This approximation consists in a truncation of the ERG equations,
which by means of a low momentum expansion leads to reasonable results.
