  We propose a unified treatment of extensions of group-valued contents (i.e.,
additive set functions defined on a ring) by means of adding new null sets. Our
approach is based on the notion of a completion ring for a content $\mu$. With
every such ring $\mathcal N$, an extension of $\mu$ is naturally associated
which is called the $\mathcal N$-completion of $\mu$. The $\mathcal
N$-completion operation comprises most previously known completion-type
procedures and also gives rise to some new extensions, which may be useful for
constructing counterexamples in measure theory. We find a condition ensuring
that $\sigma$-additivity of a content is preserved under the $\mathcal
N$-completion and establish a criterion for the $\mathcal N$-completion of a
measure to be again a measure.
