Sigma algebras plays an integral role in explaining the entire concept of measure theory, majorly because it’s a collection of subsets of a given set, whereby the subsets can be finite or infinite intriguingly, measurable functions are derived by this concept of sigma algebras. This paper provides a formidable guide towards deriving the respective measurable functions using finite sigma algebras by examining sigma algebras associated to a given set X and their corresponding measurable functions. Finite algebras will be constructed by ensuring all the axioms of algebras are satisfied.