# Properties of delta function

Consider two arbitrary sets of coordinates $$z_0$$ and $$z$$ in some space, mapped via some $$\bar{z} :$$=$$z_0 \rightarrow z$$

I have a function $$\tag{1}\rho(z)=\int\delta(z-\bar{z}(z_0))\rho_0 (z_0)dz_0$$ this will give me $$\tag{2}\rho(z)=\rho_0 (\bar{z}^{-1}(z))\frac{\partial z_0}{\partial z}$$ How to obtain equation (2) from equation (1).

• This should be what you are looking for; math.stackexchange.com/q/56939/8157 – Giuseppe Negro Dec 17 '18 at 10:40
• Also, please use the double dollar and the "\tag" command for display formulas, instead of ------ Click on "edit" to see how I have done. – Giuseppe Negro Dec 17 '18 at 10:42