When does intersection of measure 0 implies interior-disjointness?

If there are two “nice” shapes in $R^2$, such as circles or polygons, whose intersection has area 0, then they must be interior-disjoint, as their intersection can only contain pieces of their boundary.

My question is: what is a simple term for those “nice” subsets of $R^2$ for which intersection of area 0 implies interior-disjointness?

I am not looking for the most general term – just a simple term which I can use in a paper on another topic.

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