The difference between Measurable space and Measure space
When used as nouns, measurable space means a set with a σ-algebra defined on it, 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 space and Measure space
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Measurable space as a noun (mathematics):
A set with a σ-algebra defined on it.
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Measure space as a noun (analysis):
A measurable space which has a positive measure defined on its σ-algebra.