calculus – prove that a Paraboloid is a hausdorff measurable subset

I’m trying to study for my exam and the question is:


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 probleme 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.