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

Detection of Finite-Frequency Current Moments with a Dissipative Resonant Circuit