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If, for $n>2$,$\mu_n$ puts masses $n^{-1},n^{-1}, 1-2n^{-1}$toat$2n, -n, -\frac{n}{n+2}$$2n, -n, -\frac{n}{n-2}$ respectively (so that $\mu$ puts the unit mass toat(-1)$-1$), doesn't it work?
If $\mu_n$ puts masses $n^{-1},n^{-1}, 1-2n^{-1}$to$2n, -n, -\frac{n}{n+2}$ respectively (so that $\mu$ puts the unit mass to(-1)), doesn't it work?
If, for $n>2$,$\mu_n$ puts masses $n^{-1},n^{-1}, 1-2n^{-1}$at$2n, -n, -\frac{n}{n-2}$ respectively (so that $\mu$ puts the unit mass at$-1$), doesn't it work?
If $\mu_n$ puts masses $n^{-1},n^{-1}, 1-2n^{-1}$ to $2n, -n, -\frac{n}{n+2}$ respectively (so that $\mu$ puts the unit mass to (-1)), doesn't it work?