The story
The theorem is due to Dorothy Maharam.
Etymology from Wiktionary, CC BY-SA 4.0.
Maharam's theorem
Today it means: A result about the decomposability of measure spaces, playing an important role in the theory of Banach spaces. In brief, it states that every complete measure space is decomposable into "non-atomic parts" (copies of products of the unit interval [0,1] on the reals), and "purely atomic parts", using the counting measure on some discrete space. Full definition →