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.