The difference between Counting measure and Positive measure
When used as nouns, counting measure means a positive measure which, for each subset of a given measure space, assigns a value equal to the number of points in that subset, 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 Counting measure and Positive measure
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Counting measure as a noun (analysis):
A positive measure which, for each subset of a given measure space, assigns a value equal to the number of points in that subset.
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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.