  In 1948, W. Hoeffding introduced a large class of unbiased estimators called
U-statistics, defined as the average value of a real-valued k-variate function
h calculated at all possible sets of k points from a random sample. In the
present paper we investigate the corresponding extreme value analogue, which we
shall call U-max-statistics. We are concerned with the behavior of the largest
value of such function h instead of its average. Examples of U-max-statistics
are the diameter or the largest scalar product within a random sample.
U-max-statistics of higher degrees are given by triameters and other metric
invariants.
