A continuum structure function (CSF) y is a non-decreasing mapping from the unit hypercube to the unit interval. Define PÅα={x•γ(x)≥α whereas γ(y)<α for all y<x}, the set of minimal vectors to level α. This paper examines CSFs for which each PÅα is infinite. It is shown that if γ is such a CSF and X is a vector of independent random variables, the distribution of γ(X) is readily calculated. Further, if γ is an arbitrary right-continuous CSF, the distribution of γ(X) may be approximated arbitrarily closely by that of γ'(X) where γ' is a right-continuous CSF for which each minimal vector set is finite.
