The difference between Complete measure and Positive measure
When used as nouns, complete measure means a measure such that, for every set of measure zero belonging to its domain, all subsets of that set are also assigned measure zero by the given measure, 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 Complete measure and Positive measure
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Complete measure as a noun (analysis):
A measure such that, for every set of measure zero belonging to its domain, all subsets of that set are also assigned measure zero by the given measure.
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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.