Abstract
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 strengtheningbyshowingthatvarioussetsofmeasuresdefinedbyregularityproperties aregenericinthesetofallmeasuresonalocallycompactmetricspace.Asabyproduct, we obtain the fact that a generic measure on euclidean space is singular continuous.
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