  Position measurements are examined under the assumption that object position
x_t and probe position X_t just after the measurement are expressed by a linear
combination of positions x_0 and X_0 just before the measurement. The
Heisenberg uncertainty relation between the position uncertainty and momentum
disturbance holds when the measurement error \epsilon(x_t) for the object
position x_t is adopted as the position uncertainty. However, the uncertainty
in the measurement result obtained for x_0 is the standard deviation of the
measurement result, and not the measurement error \epsilon(x_0). This
difference is due to the reduction of a wave packet. The validity of the
linearity assumption is examined in detail.
