Summary
In [8] we found a class of overlapping asymmetric self-similar measures on the real line, which are generically absolutely continuous with respect to the Lebesgue measure. Here we construct exceptional measures in this class being singular.
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Neunhäuserer, J. A construction of singular overlapping asymmetric self-similar measures. Acta Math Hung 113, 333–343 (2006). https://doi.org/10.1007/s10474-006-0110-0
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DOI: https://doi.org/10.1007/s10474-006-0110-0