# Math Help - Show this set if measurable

1. ## Show this set is measurable

Let f be a function from $R^n$ to $R^+$ such that:

Uf = {(x,y): 0 < y< f(x)} is a measurable set in $R^{n+1}$

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

Suppose a > 1

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

Show $S_d$ is measurable for all d>0

I think it's because:

$S_d$ is a translation Uf $\cap$ ((a, a+d)X $R^n$), which is measurable.

Any thoughts