The difference between Measurable space and Σ-algebra
When used as nouns, measurable space means a set with a σ-algebra defined on it, 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 space and Σ-algebra
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Measurable space as a noun (mathematics):
A set with a σ-algebra defined on it.
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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.