  Without violating causality, we allow performing measurements in time reverse
process of a feedback manipulated stochastic system. As a result we come across
an entropy production due to the measurement process. This entropy production,
in addition to the usual system and medium entropy production, constitutes the
total entropy roduction of the combined system of the reservoir, the system and
the feedback controller. We show that this total entropy production of "full"
system satisfies an integrated fluctuation theorem as well as a detailed
fluctuation theorem as expected. We illustrate and verify this idea through
explicit calculation and direct simulation in two examples.
