# mg.metric geometry – Relationship between Lebesgue measure and Hausdorff metric

Let $$A, Bsubsetmathcal K(mathbb{R}^d)$$ ($$=$$ compact subsets of $$mathbb R^d$$) such that $$Asubset B$$. I would like to know if there are conditions on the sets $$A, B$$ for which
$$lambda(Bsetminus A)leq Crho (A, B)quadtext{for some} C>0,$$
where $$lambda$$ is the $$d$$-dimensional Lebesgue measure and $$rho$$ is the Hausdorff distance on $$mathcal K(mathbb R^d)$$.