English Dictionary

σ-algebra

IPA（発音記号）

/ˈsɪɡ.mə ˈæl.dʒɪ.bɹə/

名詞

(mathematical analysis) A collection of subsets of a given set, such that the empty set is part of this collection, the collection is closed under complements (with respect to the given set) and the collection is closed under countable unions.

日本語の意味

与えられた集合の部分集合全体の集まりであり、空集合を含み、各部分集合の補集合および数え上げ可能な部分集合の和集合に対して閉じている数学的な構造。

To apply the dominated convergence theorem, you must first verify that the measurable sets form a σ-algebra on the underlying space.

優収束定理を適用するためには、まず可測集合が元の空間上でシグマ代数を成すことを確認しなければならない。

意味（1）

(mathematical analysis) A collection of subsets of a given set, such that the empty set is part of this collection, the collection is closed under complements (with respect to the given set) and the collection is closed under countable unions.

Consider all the sigma-algebras that contain ℱ and take their intersection, which we call 𝛴, i.e., a subset A⊂𝛺 is in 𝛴 if and only if A is in every sigma-algebra containing ℱ. It is easy to check that 𝛴 is indeed a sigma-algebra.

σ-algebras （ plural ）