  The influence theorem for product measures on the discrete space {0,1}^N may
be extended to probability measures with the property of monotonicity (which is
equivalent to `strong positive-association'). Corresponding results are valid
for probability measures on the cube [0,1]^N that are absolutely continuous
with respect to Lebesgue measure. These results lead to a sharp-threshold
theorem for measures of random-cluster type, and this may be applied to
box-crossings in the two-dimensional random-cluster model.
