Maharam's theorem

proper noun

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.

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Meanings

proper noun
  1. mathematicsA 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.

Origin

The theorem is due to Dorothy Maharam.

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Cite this entry
APA

Maharam's theorem. (n.d.). In WatkinsX Dictionary. Retrieved November 5, 2026, from https://dictionary.watkinsx.com/word/Maharam's%20theorem

MLA

“Maharam's theorem.” WatkinsX Dictionary, https://dictionary.watkinsx.com/word/Maharam's%20theorem. Accessed November 5, 2026.

Chicago

WatkinsX Dictionary, s.v. “Maharam's theorem,” accessed November 5, 2026, https://dictionary.watkinsx.com/word/Maharam's%20theorem.

Source: Maharam's theorem on Wiktionary, CC BY-SA 4.0.