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Can anyone provide a sequence of singular (w.r.t. Lebesgue measure) measures $\in\mathcal{M}([0,1])=C[0,1]^*$ converging $weakly^*$ to an absolutely continuous (w.r.t. Lebesgue measure) measure?

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    Two small requests: 1. If you re-post a question, either [here](http://math.stackexchange.com/questions/118061/radon-nikodym-decomposition) or [on MO](http://mathoverflow.net/questions/90654/about-a-radon-measure-closed) please say that you asked the same (or a very closely related one) elsewhere. 2. Please don't introduce new tags, stick to those that are available.2012-03-10

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