Let $X=R^n$ and $Y=R^m$ be two Euclidean spaces with $m<n$. Let $\varphi$ and $\phi$ are two smooth maps from $X$ to $Y$, and $\mu$ a probability measure on $X$. Is there any relationship between $(\varphi+\phi)_\#\mu$ with $\varphi_\#\mu$ and $\phi_\#\mu$ (where $\#$ denotes the push-forward of a measure)?