Near-record observations are the ones that occur between successive record times and within a fixed distance of the current record value. In this talk, we will generalize the concept of near-record observations to the notion of observations that fall into a random region determined by a given record and a Borel set. We will describe the exact distribution of the number of such observations and establish limiting properties of this number. In addition, we will give some asymptotic results for sums of such observations. Numbers of observations falling into random regions determined by records are interesting not only from the theoretical point of view as natural extensions of numbers of near-record observations. They can find applications in different fields. During the talk we will indicate some applications of the presented theoretical results in hydrology, meteorology, insurance and record theory. In particular, we will use the new results to derive exact and asymptotic properties of inter-record times and of numbers of repetitions of records.

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