I was reading Lars Ahlfors Complex Analysis and encountered this statement from the author (p.75,76).
Let $E$ be a point set in the plane whose area $A(E) = \int\int\limits_{E} dx dy$ can be evaluated as a double integral.
If $f(z) = u(x,y) + iv(x,y)$ is a bijective differentiable mapping, then by the rule for changing integration variables the area of image $E' = f(E)$ is given by:
$A(E') =\int\int\limits_{E} |u_xv_y - u_yv_x|dxdy$.
$u_x,u_y,v_y,v_x$ are the partial derivatives.
I could not understand how the formula for $A(E')$ is derived. Any help would be appreciated.