  We calculate the full frequency spectral density of voltage fluctuations in a
Single Electron Transistor (SET), used as an electrometer biased above the
Coulomb threshold so that the current through the SET is carried by sequential
tunnel events. We consider both a normal state SET and a superconducting SET.
The whole spectrum from low frequency telegraph noise to quantum noise at
frequencies comparable to the SET charging energy $(E_{C}/\hbar)$, and high
frequency Nyquist noise is described. We take the energy exchange between the
SET and the measured system into account using a real-time diagrammatic Keldysh
technique. The voltage fluctuations determine the back-action of the SET onto
the measured system and we specifically discuss the case of superconducting
charge qubit read-out and measuring the so-called Coulomb staircase of a single
Cooper pair box.
