Instead of inspecting all programs in the UP, just inspect all programs with length less than n. As n becomes larger and larger, this covers more and more of the total probability mass in the up and the total probability mass covered this way approaches 1. What to do about the non-halting programs? Well, just run all the programs for m steps, I guess. I think this is the approximation of UP that is implied.
Instead of inspecting all programs in the UP, just inspect all programs with length less than n. As n becomes larger and larger, this covers more and more of the total probability mass in the up and the total probability mass covered this way approaches 1. What to do about the non-halting programs? Well, just run all the programs for m steps, I guess. I think this is the approximation of UP that is implied.