Exercise 5, § 5

Let $\rho, \sigma$ be two atomic measures on T, and let M, N be the smallest sets carrying $|\rho|$ and $|\sigma|$, respectively. For $\rho$ and $\sigma$ to be alien, it is necessary and sufficient that $M \cap N = \varnothing$. From this, deduce an example of an atomic measure $\nu$ on the interval $I = [0,1]$ of $\mathbf{R}$, such that I is the support of $\nu^+$ and of $\nu^-$.