sigma–ring of sets

A σ-ring of sets is a nonempty collectionMathworldPlanetmath 𝒮 of sets such that

  • if A𝒮 and B𝒮 then A-B𝒮 and

  • if Ai𝒮 for i=1,2, then i=1Ai𝒮

A σ-ring is also closed under countableMathworldPlanetmath intersectionsMathworldPlanetmath since


where A=i=1Ai.

σ-rings are used in measure theory.

Title sigma–ring of sets
Canonical name SigmaringOfSets
Date of creation 2013-03-22 17:04:34
Last modified on 2013-03-22 17:04:34
Owner Mathprof (13753)
Last modified by Mathprof (13753)
Numerical id 7
Author Mathprof (13753)
Entry type Definition
Classification msc 28A05