Hans Hahn was born on 27 September 1879 in Vienna. He initially studied law, but switched to mathematics, receiving a PhD from the University of Vienna in 1902. During his career, he held academic positions at his alma mater, the University of Vienna, and at the University of Bonn. Hahn served and was wounded in World War I. He died on 24 July 1934 in Vienna at the age of 54.
Hahn made important contributions to real analysis, functional analysis, topology and set theory. A number of important theorems bear his name, including the Hahn-Banach theorem, co-named with Stefan Banach and the Hahn decomposition theorem. The decomposition theorem is important in probability, as in other branches of analysis.