The difference between Measure space and Positive measure
When used as nouns, measure space means a measurable space which has a positive measure defined on its σ-algebra, whereas positive measure means a function whose domain is a σ-algebra, whose codomain is [0,∞], and which is countably additive.
check bellow for the other definitions of Measure space and Positive measure
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Measure space as a noun (analysis):
A measurable space which has a positive measure defined on its σ-algebra.
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Positive measure as a noun (analysis):
A function whose domain is a σ-algebra, whose codomain is [0,∞], and which is countably additive.