 He proved unique ergodicity of horocycle flows on compact hyperbolic Riemann surfaces in the early 1970s.In 1977, he gave an ergodic theory reformulation, and subsequently proof, of Szemerédi's theorem.The "Furstenberg boundary" and "Furstenberg compactification" of a locally symmetric space are named after him, as is the Furstenberg–Sárközy theorem in additive number theory.