  We present a family of entropic uncertainty relations for pointer-based
simultaneous measurements of conjugate observables. The lower bounds of these
relations explicitly incorporate the influence of the measurement apparatus. We
achieve this by using a mathematical theorem which states that the information
entropy of convoluted probability distributions is bound from below. As a
consequence of these results we can straightforwardly show that appropriately
squeezed states are minimal entropy states for simultaneous measurements.
