  We propose a definition of mass for characteristic hypersurfaces in
asymptotically vacuum space-times with non-vanishing cosmological constant
$\Lambda \in {\mathbb R}^*$, generalising the definition of Trautman and Bondi
for $\Lambda=0$. We show that our definition reduces to some standard
definitions in several situations. We establish a balance formula linking the
characteristic mass and a suitably defined renormalised volume of the null
hypersurface, generalising the positivity identity of one of us (PTC) and Paetz
proved when $\Lambda=0$.
