  Determining the work which is supplied to a system by an external agent,
provides a crucial step in any experimental realization of transient
fluctuation relations. This, however, poses a problem for quantum systems,
where the standard procedure requires the projective measurement of energy at
the beginning and the end of the protocol. Unfortunately, projective
measurements, which are preferable from the point of view of theory, seem to be
difficult to implement experimentally. We demonstrate that, when using a
particular type of generalized energy measurements, the resulting work
statistics is simply related to that of projective measurements. This relation
between the two work statistics entails the existence of modified transient
fluctuation relations. The modifications are exclusively determined by the
errors incurred in the generalized energy measurements. They are universal in
the sense that they do not depend on the force protocol. Particularly simple
expressions for the modified Crooks relation and Jarzynski equality are found
for Gaussian energy measurements. These can be obtained by a sequence of
sufficiently many generalized measurements which need not be Gaussian. In
accordance with the central limit theorem, this leads to an effective error
reduction in the individual measurements, and even yields a projective
measurement in the limit of infinite repetitions.
