In mathematics, a representation theorem is a theorem that states that every abstract structure with certain properties is isomorphic to another (abstract or concrete) structure. For example, * in algebra, * Cayley's theorem states that every group is isomorphic to a transformation group on some set. Representation theory studies properties of abstract groups via their representations as linear transformations of vector spaces. * Stone's representation theorem for Boolean algebras states that every Boolean algebra is isomorphic to a field of sets. A variant, Stone's representation theorem for lattices states that every distributive lattice is isomorphic to a sublattice of the power set lattice of some set. Another variant, states that there exists a duality (in the sense of an arro