Some of your past answers have not been well-received, and you're in danger of being blocked from answering. In mathematics, a positive (or signed) measure μ defined on a σ-algebra Σ of subsets of a set X is called a finite measure if μ(X) is a finite real number (rather than ∞), and a set A in Σ is of finite measure if μ(A) < ∞. Among finite measures are probability measures . A measure μ is called σ-finite if X can be decomposed into a countable union of measurable sets of finite measure. The finite measures are often easier to handle than more general measures and show a variety of different properties depending on the sets they are defined on. The s-finite measures should not be confused with the σ-finite (sigma-finite) measures. In mathematics, a non-measurable set is a set which cannot be assigned a meaningful "volume".

For example, the real numbers with the standard Lebesgue measure are σ-finite but not finite. Almost all non-negative real numbers have only finitely many multiple lies in a measurable set with finite measure The measure μ

The finite measures are often easier to handle than more general measures and show a variety of different properties depending on the … The mathematical existence of such sets is construed to provide information about the notions of length, area and volume in formal set theory. Please pay close attention to the following guidance: Please be sure to answer the question.Provide details

For example, Lebesgue measure on the real numbers is not finite, but it is σ-finite. Indeed, consider the intervals [k, k + 1) for all integers k; there are countably many such intervals, each has measure 1, and their union is the entire real line. In measure theory, a branch of mathematics that studies generalized notions of volumes, an s-finite measure is a special type of measure. An s-finite measure is more general than a finite measure, but allows one to generalize certain proofs for finite measures. Analogously, a set in a measure space is said to have a σ-finite measure if it is a countable union of sets with finite measure. In measure theory, a branch of mathematics, a finite measure or totally finite measure is a special measure that always takes on finite values. In measure theory, a branch of mathematics, a finite measure or totally finite measure [1] is a special measure that always takes on finite values. Among finite measures are probability measures.