The difference between Measurable set and Measure space

When used as nouns, measurable set means a subset of a given measurable space which is a member of the σ-algebra of that space, whereas measure space means a measurable space which has a positive measure defined on its σ-algebra.


check bellow for the other definitions of Measurable set and Measure space

  1. Measurable set as a noun (analysis):

    A subset of a given measurable space which is a member of the σ-algebra of that space.

  1. Measure space as a noun (analysis):

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