== σ-finite measure == 

 [Wikipedia] A positive (or signed) measure μ defined on a σ-algebra Σ of subsets of a set X is called finite if μ(X) is a finite real number (rather than ∞). The measure μ is called σ-finite if X is the countable union of measurable sets of finite measure.  A set in a measure space is said to have σ-finite measure if it is a countable union of sets with finite measure.