  A measurement on a section K of the set of states of a finite dimensional
C*-algebra is defined as an affine map from K to a probability simplex. Special
cases of such sections are used in description of quantum networks, in
particular quantum channels. Measurements on a section correspond to
equivalence classes of so-called generalized POVMs, which are called quantum
testers in the case of networks. We find extremality conditions for
measurements on K and characterize generalized POVMs such that the
corresponding measurement is extremal. These results are applied to the set of
channels. We find explicit extremality conditions for two outcome measurements
on qubit channels and give an example of an extremal qubit 1-tester such that
the corresponding measurement is not extremal.
