  We present a new method for describing quantum measurements in relativistic
systems that applies (i) to any QFT and for any field-detector coupling, (ii)
to the measurement of any observable, and (iii) to arbitrary size, shape and
motion of the detector. We explicitly construct the probabilities associated to
$n$ measurement events, while treating the spacetime coordinates of the events
are random variables. These probabilities define a linear functional of a $2n$
unequal time correlation function of the field, and thus, they are Poincar\'e
covariant. The probability assignment depends on the properties of the
measurement apparatuses, their state of motion, intrinsics dynamics, initial
states and couplings to the measured field. For each apparatus, this
information is contained in a function, the detector kernel, that enters into
the probability assignment. In a companion paper, we construct the detector
kernel for different types of measurement.
