## order of integration

How do you justify that $\int_{0}^{\infty}\int_{x}^{\infty}\int_{x}^{\infty }\frac{\cos ay}{y}\frac{\cos bz}{z}\ dz\ dy\ dx$

$=\int_{0}^{\infty}\int_{0}^{\infty}\int_{0}^{\text {min} \{y,z\}}\frac{\cos ay}{y}\frac{\cos bz}{z}\ dx\ dy\ dz\ \ \ a,b >0$ ?

Neither integral converges absolutely.