In this study, the Hammersley-Chapman-Robbins bounds provide tighter lower limits on the estimator's variance than the Cramér–Rao bound under the given regularity conditions.

The variable fluctuated boundedly around its mean, never exceeding fixed limits.

The boundedness of the solution set made it easier to apply compactness arguments.

The seminar compared the boundednesses of different function spaces to illustrate how compactness varies.