  We generalize the ham sandwich theorem for the case of well separated
measures. Given convex bodies $K_1,...,K_d$ in $\mathbb{R_d}$ and numbers
$\alpha_1,...,\alpha_d \in [0, 1]$, we give a sufficient condition for
existence and uniqueness of an (oriented)halfspace H with Vol($H \cap K_i$)=
$\alpha_i \dot$ Vol$K_i$ for every i. The result is extended from convex bodies
to measures.
