  When the chemical potential of an electron system has a discontinuity at a
density $n^{*}$, the system is said to be incompressible and a finite energy is
required to create mobile charges in the bulk of the system. The quantum Hall
effect is associated with incompressibilities in a two-dimensional electron
system that occur at magnetic-field dependent densities, $n^{*}(B)$. In these
notes we discuss two aspects of the physics of quantum Hall systems that follow
directly from this association.
