## Jordan measurability of the level sets of a function

Hello all,

Let $F : R^n -> R$ be a continuous function, what conditions may be imposed on $F$, so that the levels sets {$x : F(x) = \alpha$} are Jordan measurable for all $\alpha$.

In my case, I know that $F$ is Lipschitz continuous, so I think the level sets are Jordan measurable for all by countable number of $\alpha$, but I would like to have it for all $\alpha$.

This question is related to http://mathoverflow.net/questions/58327/jordan-measurability-of-the-level-sets, but approaches the problem from somewhat different point of view.

Thanks a lot,

Shay.

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