We show that geometric disorder leads to some purely singular continuous spectrum generically. The main input is a result of Simon known as the Wonderland theorem in [17, Section 2]. 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 the fact that a generic measure on euclidean space is singular continuous