Sigma-Algebra

A sigma-algebra is a mathematical structure used to define and manage collections of subsets within a set, especially in probability and measure theory. It is a collection of subsets closed under operations such as taking complements, countable unions, and countable intersections. This means if a set is in the collection, then so are its complement and the union or intersection of countably many sets in the collection. Sigma-algebras provide a rigorous framework to handle “events” and their probabilities or measures systematically, ensuring that the collection of subsets behaves predictably and consistently for analysis.