Sigma-additive set function

A sigma-additive set function, often referred to in the context of measure theory, is a type of function defined on a σ-algebra (sigma-algebra) of subsets of a given set. This function satisfies a specific property related to countable additivity, which is a fundamental concept in measure theory. **Definition:** Let \( \mu \) be a set function defined on a σ-algebra \( \mathcal{F} \) of subsets of a set \( X \).