  We consider the measurement of higher current moments with a dissipative
resonant circuit, which is coupled inductively to a mesoscopic device in the
coherent regime. Information about the higher current moments is coded in the
histograms of the charge on the capacitor plates of the resonant circuit.
Dissipation is included via the Caldeira-Leggett model, and it is essential to
include it in order for the charge fluctuations (or the measured noise) to
remain finite. We identify which combination of current correlators enter the
measurement of the third moment. The latter remains stable for zero damping.
Results are illustrated briefly for a quantum point contact.
