Skip to main content
MathOverflow

Return to Question

Bumped by Community user
Bumped by Community user
Bumped by Community user
Bumped by Community user
corrected the English
Source Link
edit approved Nov 13, 2015 at 23:06
Fly by Night
edit approved Nov 13, 2015 at 23:06
Fly by Night
  • 310
  • 2
  • 8

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

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)?

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)?

Source Link
Hongdmhut Hong
Hongdmhut Hong
  • 31
  • 2

Push-forward of sum of two maps

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)?