English Dictionary

Maharam's theorem

固有名詞

(mathematics) 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.

日本語の意味

（数学、測度論の文脈で）マハラムの定理は、完備測度空間がその測度の性質に応じて、非原子的な部分と純粋に原子的な部分に分解できることを示す定理です。非原子的部分は、[0,1]の区間の積空間のような構造を持ち、純粋に原子的な部分は、離散空間上の計数測度によって特徴づけられます。

Maharam's theorem shows that any complete measure space can be decomposed into non-atomic parts (copies of products of the unit interval [0,1]) and purely atomic parts with the counting measure, a fact that plays an important role in the theory of Banach spaces.

任意の完備測度空間が、単位区間[0,1]の積に相当する非原子的部分と、カウント測度を備えた純粋に原子的な部分に分解できるという定理は、バナッハ空間論において重要な役割を果たします。

意味（1）

(mathematics) 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.