 The notion turned out to have applications in areas such as number theory, fractals, signal processing and electrical engineering.In his 1977 paper, "Ergodic behavior of diagonal measures and a theorem of Szemerédi on arithmetic progressions", Furstenberg used methods from ergodic theory to prove a celebrated result by Endre Szemerédi, which states that any subset of integers with positive upper density contains arbitrarily large arithmetic progressions.His insights led to important results, such as the proof by Ben Green and Terence Tao that the sequence of prime numbers includes arbitrary large arithmetic progressions.