Banach lattice
In the mathematical disciplines of in functional analysis and order theory, a Banach lattice (X,‖·‖) is a complete normed vector space with a lattice order,[3] Every Banach lattice admits a continuous approximation to the identity.[4] A Banach lattice satisfying the additional conditionSuch spaces, under the assumption of separability, are isomorphic to closed sublattices of L1([0,1]).[5] The classical mean ergodic theorem and Poincaré recurrence generalize to abstract (L)-spaces.