Can one probe the structure function of the pomeron?

We discuss whether the diffractive structure functions defined by current experiments at HERA are indeed probing the partonic structure function of the pomeron. We observe that the {\it pseudorapidity} cuts commonly employed require that the struck parton in the pomeron be far off mass shell in sizeable regions of parameter space. As a result an interpretation in terms of constituent partons within the pomeron is inadequate. One may nevertheless use a partonic description for the {\it amplitude} for virtual photon-pomeron scattering to compute a diffractive structure function for pseudorapidity gap events. The resulting form may have significant scaling violation.