The positive definite character of the covariance function
entails the following properties:
, an a priori variance cannot
be negative;
, the covariance is an even function;
, Schwarz's inequality.
Since the degree of correlation between two variables 
and
generally decreases as the distance 
between them increases, so, in
general, does the covariance function, which decreases from its value at
the origin 
. Correspondingly, the semi-variogram
increases from its value at the origin,
.