  We propose a derivation of the full counting statistics of electronic current
based on a positive-operator-valued measure. Our approach justifies the
Levitov-Lesovik formula in the long-time limit, but can be generalized to the
detection of finite-frequency noise correlations. The combined action of the
projection postulate and the quantum formula for current noise at high
frequencies imply an additional white noise. Estimates for this additional
noise are in accordance with known experiments. We propose an experimental test
of our conjecture by a simultaneous measurement of high- and low-frequency
noise.
