• convergence in proba and almost surely
• permutation p values
• convergence in proba and weakly

Things I need to clarify:

• monte carlo permutation p values vs fully enumerating the group: where does taking more monte carlo samples help? Presumably it gives you more confidence in the result, but where does that pop up in the statistical wording?
• In RCT, where does the randomization appear in the statistical analysis? Or is it something out of the domain of statistics and only used for causal inference (whatever that means)?