The difference between Measurable set and Measure 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 measure space means a measurable space which has a positive measure defined on its σ-algebra.
check bellow for the other definitions of Measurable set and Measure 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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Measure space as a noun (analysis):
A measurable space which has a positive measure defined on its σ-algebra.