Order of Monte Carlo integration and frequency summation

Question

I am currently trying to calculate an integration formula of a linear response function by Monte Carlo method. It is a multiple integration over three 3D vectors, i.e., nine dimensions in all. And because of green function, there will also be an infinite discete frequency summation. This can be done either inside the integral, i.e., when evaluating the integrand, or outside the integral, i.e., summing up the integral result for each discete frequency point.

My question is that whether this order issue matters or not.

This post imported from StackExchange Physics at 2014-08-22 05:08 (UCT), posted by SE-user huotuichang

Comments

The order does not matter for finite discrete summations. When infinities or integrals are involved, the order may matter.

This post imported from StackExchange Physics at 2014-08-22 05:08 (UCT), posted by SE-user leongz