I'm trying to study for my exam and the question is:
Let
$A=\{ ( x,y,z) R^3 : || (x,y )|| , z=1/2 ||( x,y )||^2\}$
Show that $A$ is a $H^2$ - measurable subset and calculate the surface area.
I don't have a problem computing the surface area but I don't know how to show the first part.
I would be really thankful if someone could give me a hint.