You are here
Home ›product $\sigma$-algebra
Primary tabs
product -algebra
Given measurable spaces and , the product -algebra is defined to be the -algebra on the Cartesian product generated by sets of the form for and .
More generally, the product -algebra can be defined for an arbitrary number of measurable spaces , where runs over an index set . The product is the -algebra on the generalized cartesian product generated by sets of the form where for all , and for all but finitely many . If are the projection maps, then this is the smallest -algebra with respect to which each is measurable.
Keywords:
$\sigma$-algebra,cartesian product
Related:
ProductMeasure,InfiniteProductMeasure
Synonym:
product sigma-algebra
Major Section:
Reference
Type of Math Object:
Definition
Parent:
Mathematics Subject Classification
28A60 Measures on Boolean rings, measure algebras- Forums
- Planetary Bugs
- HS/Secondary
- University/Tertiary
- Graduate/Advanced
- Industry/Practice
- Research Topics
- LaTeX help
- Math Comptetitions
- Math History
- Math Humor
- PlanetMath Comments
- PlanetMath System Updates and News
- PlanetMath help
- PlanetMath.ORG
- Strategic Communications Development
- The Math Pub
- Testing messages (ignore)
- Other useful stuff
Recent Activity
May 24
new correction: typo? by Filipe
May 22
new question: Linear Algebra Combination Problem! by Aleph Zero
new question: Computation of $\varphi(2000)$ by unlord
May 21
new question: pure subgroups by lvoyster
new correction: Typo in M\"obius function? by Aleph Zero
new collection: analytic number theory by Aleph Zero
May 20
new question: Taylor's Series Query! by unlord
new question: Laplace transform by J
new question: Residue Calculus by J
May 19
new Education: Project: PlanetMath Outlines Series by unlord
new correction: typo? by Filipe
May 22
new question: Linear Algebra Combination Problem! by Aleph Zero
new question: Computation of $\varphi(2000)$ by unlord
May 21
new question: pure subgroups by lvoyster
new correction: Typo in M\"obius function? by Aleph Zero
new collection: analytic number theory by Aleph Zero
May 20
new question: Taylor's Series Query! by unlord
new question: Laplace transform by J
new question: Residue Calculus by J
May 19
new Education: Project: PlanetMath Outlines Series by unlord


