sigma algebra

A sigma algebra (or σ-algebra) is to set algebras what sigma males are to males. The Borel hierarchy (the analog of the male hierarchy) is not a σ-algebra at any countable rank; instead the σ-algebra has the largest possible rank -- ω_1, the least uncountable ordinal (under suitable conditions e.g. the Polish space is uncountable. This is known as the non-collapse of the Borel hierarchy).

A σ-algebra is closed under countable union, countable intersection, and relative complement. This means σ-algebras arise naturally in the study of measure theory, where the measurable sets form a σ-algebra.

The algebra of Lebesgue-measurable subsets of R (i.e. the sets of real numbers with a well-defined "length", which is possibly infinity) form a sigma algebra.

俚语	sigma algebra
释义	sigma algebra A sigma algebra (or σ-algebra) is to set algebras what sigma males are to males. The Borel hierarchy (the analog of the male hierarchy) is not a σ-algebra at any countable rank; instead the σ-algebra has the largest possible rank -- ω_1, the least uncountable ordinal (under suitable conditions e.g. the Polish space is uncountable. This is known as the non-collapse of the Borel hierarchy). A σ-algebra is closed under countable union, countable intersection, and relative complement. This means σ-algebras arise naturally in the study of measure theory, where the measurable sets form a σ-algebra. The algebra of Lebesgue-measurable subsets of R (i.e. the sets of real numbers with a well-defined "length", which is possibly infinity) form a sigma algebra.
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