Let f be a function from to such that:

Uf = {(x,y): 0 < y< f(x)} is a measurable set in

The following I am copying exactly as I have it in my notes:

Suppose a > 1

Let = {(x, y-a): f(x) > a, 0 < y < (f(x) -a)/d and 0 < y < 1}

Show is measurable for all d>0

I think it's because:

is a translation Uf ((a, a+d)X ), which is measurable.

Any thoughts