I want to apply to Fubini's theorem to the following integral: $$ \int_{|x-y|\geq r}\int_{a|x-y|}^{b|x-y|}|f(y)||h(t)|dtdy, $$ where $a,b,t>0,~~a<b$ and $x,y\in \mathbb{R}^n$.
My answer is the following. But i am not sure if this one is true?
$$ \int_{|x-y|\geq r}\int_{a|x-y|}^{b|x-y|}|f(y)||h(t)|dtdy=\int_{r}^{\infty}|h(t)|\left(\int_{r\le |x-y|<\frac{t}{a} }|f(y)|dy\right)dt. $$