Английская Википедия:Cylindrical σ-algebra
In mathematics — specifically, in measure theory and functional analysis — the cylindrical σ-algebra[1] or product σ-algebra[2][3] is a type of σ-algebra which is often used when studying product measures or probability measures of random variables on Banach spaces.
For a product space, the cylinder σ-algebra is the one that is generated by cylinder sets.
In the context of a Banach space <math>X,</math> the cylindrical σ-algebra <math>\operatorname{Cyl}(X)</math> is defined to be the coarsest σ-algebra (that is, the one with the fewest measurable sets) such that every continuous linear function on <math>X</math> is a measurable function. In general, <math>\operatorname{Cyl}(X)</math> is not the same as the Borel σ-algebra on <math>X,</math> which is the coarsest σ-algebra that contains all open subsets of <math>X.</math>
See also
References
- Шаблон:Cite book (See chapter 2)
Шаблон:Measure theory Шаблон:Banach spaces Шаблон:Functional analysis
