An easy proof of the Stone-von Neumann-Mackey Theorem

The Stone-von Neumann-Mackey Theorem for Heisenberg groups associated to locally compact abelian groups is proved using the Peter-Weyl Theorem and the theory of Fourier transforms for Rn. A theorem of Pontryagin and van Kampen on the structure of locally compact abelian groups (which is evident in any particular case) is assumed.