  Distributionally robust optimization involves various probability measures in
its problem formulation. They can be bundled to constitute a risk functional.
For this equivalence, risk functionals constitute a fundamental building block
in distributionally robust stochastic programming. Multistage programming
requires conditional versions of risk functionals to re-assess future risk
after partial realizations and after preceding decisions.
  This paper discusses a construction of the conditional counterpart of a risk
functional by passing its genuine characteristics to its conditional
counterparts. The conditional risk functionals turn out to be different from
the nested analogues of the original (law invariant) risk measure. It is
demonstrated that the initial measure and its nested decomposition can be used
in a distributionally robust multistage setting.
