Freiman's theorem is a result in additive combinatorics that deals with sets of integers. It states that if a finite set of integers has a small sumset, meaning the set of all possible sums of pairs of its elements is not too large, then the original set can be closely approximated by an arithmetic progression. This means that the integers in the set are structured in a way that resembles a linear sequence. The theorem is named after the mathematician G. Freiman, who first formulated it in the 1970s. It has important implications in various areas of mathematics, including number theory and combinatorial geometry, as it helps to understand the additive properties of sets and their structure.