出典:Wiktionary
出典:Wikipedia
出典:『Wikipedia』 (2011/07/04 15:04 UTC 版)
In mathematics, a σ-algebra (also sigma-algebra, σ-field, sigma-field) is a technical concept for a collection of sets satisfying certain properties. The main use of σ-algebras is in the definition of measures; specifically, a σ-algebra is the collection of sets over which a measure is defined. This concept is important in mathematical analysis as the foundation for Lebesgue integration, and in probability theory, where it is interpreted as the collection of events which can be assigned probabilities.