Let $X=R^n$ and $Y=R^m$ are two Euclidean spaces with $m<n$. Let $\varphi$ and $\phi$ are two (smooth) maps from $X$ to $Y$ and $\mu$ is 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)?