  The most general change of variables theorem for the Riemann integral of
functions of a single variable has been published in 1961 (by Kestelman). In
this theorem, the substitution is made by an `indefinite integral', that is, by
a function of the form (t\mapsto c+\int_a^tg=:G(t)) where (g) is Riemann
integrable on ([a,b]) and (c) is any constant. We prove a multidimensional
generalization of this theorem for the case where (G) is injective -- using the
fact that the Riemann primitives are the same as those Lipschitz functions
which are almost everywhere strongly differentiable in ((a,b)). We prove a
generalization of Sard's lemma for Lipschitz functions of several variables
that are almost everywhere strongly differentiable, which enables us to keep
all our proofs within the framework of the Riemannian theory which was our aim.
