In order to use the Lebesgue Transformation Formula, I need to find a $V$ to exclude, but I am unsure of how exactly to do it.
Example:
Spherical Coordinates
$\Phi: \mathbb R_{>0 }\times]0,\pi[\times]0,2\pi[\to\mathbb R^{3}-V$
I have been told $V:=\mathbb R_{\geq 0}\times \{0\}\times \mathbb R$
which seems intuitive
But then I get to a point of confusion when:
Cylindrical coordinates:
$\Phi: \mathbb R_{>0 }\times]0,2\pi[\times \mathbb R\to\mathbb R^{3}-V$
BUT
$V:=\{0\}\times\mathbb R_{\geq 0}\times \mathbb R$
Why has the excluded $V$ changed from the $y-$ to the $x-$axis?