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The rare gas discharge lamp is supplied with a current, which is lower than the rated current, the voltage of the rare gas discharge lamp is determined at this instant and the swing width of this voltage is measured. A comparator for comparing measured values of the swing width of the voltage of the rare gas discharge lamp when the current control supplies a reduced current, which is lower than the rated current. A service life converter for converting the difference value output by the comparison means into an indication of the service life of the rare gas discharge lamp.