The difference between Measurable set and Σ-algebra
When used as nouns, measurable set means a subset of a given measurable space which is a member of the σ-algebra of that space, whereas σ-algebra means a collection of subsets of a given set, such that the empty set is part of this collection, the collection is closed under complements (with respect to the given set) and the collection is closed under countable unions.
check bellow for the other definitions of Measurable set and Σ-algebra
-
Measurable set as a noun (analysis):
A subset of a given measurable space which is a member of the σ-algebra of that space.
-
Σ-algebra as a noun (analysis):
A collection of subsets of a given set, such that the empty set is part of this collection, the collection is closed under complements (with respect to the given set) and the collection is closed under countable unions.