Consistency of a uniquely bracketed zero (source code)

= Consistency of a uniquely bracketed zero

Suppose random continuous real functions have unique zeros. If pointwise <convergence in probability> gives opposite strict limiting signs at the two ends of every sufficiently small interval about the target, the <intermediate value theorem> traps their zeros in those intervals with <probability> tending to one. The limiting function need not be continuous and the random functions need not be monotone.