  It is proven by explicit construction that regularization by dimensional
reduction can be formulated in a mathematically consistent way. In this
formulation the quantum action principle is shown to hold. This provides an
intuitive and elegant relation between the D-dimensional Lagrangian and Ward or
Slavnov-Taylor identities, and it can be used in particular to study to what
extent dimensional reduction preserves supersymmetry. We give several examples
of previously unchecked cases.
