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


$\displaystyle =\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.