# linear algebra – lower dimensional volume in transformation

it's a well known fact that if $$K$$ is a measurable set in $$R ^ n$$ (we can limit to convex bodies if you want), and $$T$$ a linear transformation then
$$| TK | = | detT || K |.$$
Yes $$K$$ is not $$n-$$dimensional then this equality gives $$0 = 0.$$ But $$K$$ some $$m$$– dimensional volume, $$m . Is there a similar relationship for the $$m$$three-dimensional volume of $$TK$$?