  A simple proof is given for a generalized form of a theorem of Soshnikov. The
latter states that the Janossy densities for multilevel determinantal ensembles
supported on measurable subspaces of a set of measure spaces are constructed by
dualization of bases on dual pairs of N-dimensional function spaces with
respect to a pairing given by integration on the complements of the given
measurable subspaces. The generalization extends this to dualization with
respect to measures modified by arbitrary sets of weight functions.
