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<jats:title>summary</jats:title><jats:p>Recent work has considered properties of the number of observations <jats:italic>X<jats:sub>j</jats:sub></jats:italic>, independently drawn from a discrete law, which equal the sample maximum <jats:italic>X</jats:italic><jats:sub>(n)</jats:sub> The natural analogue for continuous laws is the number <jats:italic>K<jats:sub>n</jats:sub></jats:italic>(<jats:italic>a</jats:italic>) of observations in the interval (<jats:italic>X</jats:italic><jats:sub>(n)</jats:sub>–<jats:italic>a</jats:italic>, <jats:italic>X</jats:italic><jats:sub>(n)</jats:sub>], where <jats:italic>a</jats:italic> > 0. This paper derives general expressions for the law, first moment, and probability generating function of <jats:italic>K<jats:sub>n</jats:sub></jats:italic>(<jats:italic>a</jats:italic>), mentioning examples where evaluations can be given. It seeks limit laws for <jats:italic>n</jats:italic>→ and finds a central limit result when <jats:italic>a</jats:italic> is fixed and the population law has a finite right extremity. Whenever the population law is attracted to an extremal law, a limit theorem can be found by letting <jats:italic>a</jats:italic> depend on <jats:italic>n</jats:italic> in an appropriate manner; thus the limit law is geometric when the extremal law is the Gumbel type. With these results, the paper obtains limit laws for ‘top end’ spacings <jats:italic>X</jats:italic><jats:sub>(n)</jats:sub> ‐ <jats:italic>X</jats:italic><jats:sub>(n‐j)</jats:sub> with <jats:italic>j</jats:italic> fixed.</jats:p>