Suppose is a set and is a σ-algebra of subsets of .
A σ-ideal of is a subset that is closed under countable unions and passage to subsets: if , , and , then .
If is a measure on a measurable space , then
is a σ-ideal.
Sometimes we do not have a canonical measure at our disposal, but we do have a canonical σ-ideal of negligible sets. This is the case, for example, for smooth manifolds and locally compact groups.
Replacing the data of a measure with the data of a σ-ideal results in the concept of an enhanced measurable space . See the article categories of measure theory for more details and motivation.
Created on May 3, 2024 at 03:30:46. See the history of this page for a list of all contributions to it.