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

  1. Measure space as a noun (analysis):

    A measurable space which has a positive measure defined on its σ-algebra.

  1. Positive measure as a noun (analysis):

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