We propose a definition of mass for characteristic hypersurfaces in
asymptotically vacuum space-times with non-vanishing cosmological constant
Λ ∈ R
∗
, generalising the definition of Trautman and Bondi for Λ = 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 Λ = 0.