The difference between Measurable set and Measurable space
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 measurable space means a set with a σ-algebra defined on it.
check bellow for the other definitions of Measurable set and Measurable space
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Measurable set as a noun (analysis):
A subset of a given measurable space which is a member of the σ-algebra of that space.
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Measurable space as a noun (mathematics):
A set with a σ-algebra defined on it.