  The class of norm-dependent Random Matrix Ensembles is studied in the
presence of an external field. The probability density in those ensembles
depends on the trace of the squared random matrices, but is otherwise
arbitrary. An exact mapping to superspace is performed. A transformation
formula is derived which gives the probability density in superspace as a
single integral over the probability density in ordinary space. This is done
for orthogonal, unitary and symplectic symmetry. In the case of unitary
symmetry, some explicit results for the correlation functions are derived.
