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

  1. 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.

  1. Positive measure as a noun (analysis):

    A function whose domain is a σ-algebra, whose codomain is [0,∞], and which is countably additive.