  Sample reuse techniques have significantly reduced the numerical complexity
of probabilistic robustness analysis. Existing results show that for a nested
collection of hyper-spheres the complexity of the problem of performing $N$
equivalent i.i.d. (identical and independent) experiments for each sphere is
absolutely bounded, independent of the number of spheres and depending only on
the initial and final radii.
  In this chapter we elevate sample reuse to a new level of generality and
establish that the numerical complexity of performing $N$ equivalent i.i.d.
experiments for a chain of sets is absolutely bounded if the sets are nested.
Each set does not even have to be connected, as long as the nested property
holds. Thus, for example, the result permits the integration of deterministic
and probabilistic analysis to eliminate regions from an uncertainty set and
reduce even further the complexity of some problems. With a more general view,
the result enables the analysis of complex decision problems mixing real-valued
and discrete-valued random variables.
