An example for converse of a theorem in Rudin

A theorem of Rudin's real and complex analysissuppose $\mu$ and $\nu_1$,$\nu_2$ are measures on a $\sigma$_algebra m, and $\mu$ is positive:

if $\nu_1<<\mu$ and $\nu_2\perp\mu$, then $\nu_1\perp\nu_2$ .

I would like to the converse of this theorem, for that matter, give an example.I have tried but unfortunately I could not do it. Any hints would be appreciated.