Generic sets in spaces of measures and generic singular continuous   spectrum for Delone Hamiltonians
  We show that geometric disorder leads to purely singular continuous spectrum generically.   The main input is a result of Simon known as the ``Wonderland theorem''. Here, we provide an alternative approach and actually a slight strengthening by showing that various sets of measures defined by regularity properties are generic in the set of all measures on a locally compact metric space.   As a byproduct we obtain that a generic measure on euclidean space is singular continuous. 
Daniel Lenz and Peter Stollmann