  Following Mal\'y's definition of absolutely continuous functions of several
variables, we consider $Q$-absolutely continuous mappings $f\colon X\to V$
between a doubling metric measure space $X$ and a Banach space $V$. The
relation between these mappings and Sobolev mappings $f\in N^{1,p}(X;V)$ for
$p\ge Q$ is investigated. In particular, a locally $Q$-absolutely continuous
mapping on an Ahlfors $Q$-regular space is a continuous mapping in
$N^{1,Q}_{\rm{loc}}(X;V)$, as well as differentiable almost everywhere in terms
of Cheeger derivatives provided $V$ satisfies the Radon-Nikodym property.
Conversely, though a continuous Sobolev mapping $f\in N^{1,Q}_{\rm{loc}}(X;V)$
is generally not locally $Q$-absolutely continuous, this implication holds if
$f$ is further assumed to be pseudomonotone. It follows that pseudomonotone
mappings satisfying a relaxed quasiconformality condition are also
$Q$-absolutely continuous.
