"Normal" $p$-adic Numbers?

Question

We say that a real number $x$ is normal in base $b$ if every string of $n$ digits appears with density $b^{-n}$ in $x$'s base $b$ expansion. It seems like it would be easy to generalize this notion to $p$-adic numbers, say if every string of $n$ digits appears with density $p^{-n}$. I wanted to see what is known about the subject, but "normal $p$-adic numbers" isn't yielding anything. Is there a different term for this notion?