# theoretical measure – Hausdorff dimension and functions \$ W ^ {1,1} \$

What can be said of the Hausdorff dimension of the image of a set by a $$W ^ {1,1}$$ map?

In other words,
what is the relationship between
$$mathrm {dim} _H f (A)$$ and $$mathrm {dim} _H A$$, or $$f in W ^ {1,1}$$?

Is the result also valid if $$f$$ is a BV function?