  We consider the counting statistics of electron transport through a double
quantum dot with special emphasis on the dephasing induced by a nearby charge
detector. The double dot is embedded in a dissipative enviroment, and the
presence of electrons on the double dot is detected with a nearby quantum point
contact. Charge transport through the double dot is governed by a non-Markovian
generalized master equation. We describe how the cumulants of the current can
be obtained for such problems, and investigate the difference between the
dephasing mechanisms induced by the quantum point contact and the coupling to
the external heat bath. Finally, we consider various open questions of
relevance to future research.
