## Definable measure preserving $p$-adic semialgebraic isomorphisms

Hello, This is related to my other question "http://mathoverflow.net/questions/77072/definable-measure-preserving-isomorphisms-of-p-adic-semialgebraic-sets" (sorry I do not know how to make a link).

But this time my question is: Given an open $p$-adic semialgebraic definable set $Z$ in $K^n$ (where $K$ is a $p$-adic field) can we show there cannot be a measure preserving analytic semialgebraic bijection $Z \to Z \setminus C$ where $C$ HAS NONEMPTY INTERIOR in $K^n$?

Thank you

Update2: Can we show there is no isomorphism $K^n \to K^n\setminus B$ where $B$ is a ball in $K^n$?

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