A question about the Lorentz transformation of "infinitesimals"

Notations conventions: $p$ stands for the momentum (so $d^3p$ is the differential element according to which we integrate, for the $3$ space coordinates). A Lorentz transformation is denoted by $Lambda$. I denote $vec p = (p^0,p^1,p^2,p^3)$ the 4-vector energy-momentum while I denote $p$ the spacial momentum.

I was reading a course about QFT, and inside an integral $int u(vec p)d^3p$, after the use of substitution $p leftrightarrow Lambda p$, they use this relation:

$$
dfrac{d^3(Lambda p)}{(Lambda p)^0} = dfrac{d^3p}{p^0}
$$

It seems to be pretty obvious for the author, so I might have missed something.

I know that $p^0 = sqrt{m^2 + p^2}$ and $(Lambda p)^0 = sqrt{m^2 + (Lambda p)^2}$ (where I use the notation convention for a 3-vector $p$, $p^2 = pcdot p$)
How do you derive this relation?