Diophantine approximation
Aleksandr Khinchin proved in 1926 that if the series formula_20 diverges, then almost every real number (in the sense of Lebesgue measure) is formula_21-approximable, and if the series converges, then almost every real number is not formula_21-approximable. The circle of ideas surrounding this theorem and its relatives is known as "metric Diophantine approximation" or the "metric theory of Diophantine approximation" (not to be confused with height "metrics" in Diophantine geometry) or "metric number theory".