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?
A sequence of singular measures converging weakly* to a continuous measure
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real-analysis
functional-analysis
measure-theory
singular-measures
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