In mathematics, specifically in order theory and functional analysis, an **abstract L-space**, an

In probability theory, it means the standard probability space.^{[2]}

The strong dual of an AM-space with unit is an AL-space.^{[1]}

The reason for the name abstract *L*-space is because every AL-space is isomorphic (as a Banach lattice) with some subspace of ^{[1]}
Every AL-space *X* is an order complete vector lattice of minimal type;
however, the order dual of *X*, denoted by *X*^{+}, is *not* of minimal type unless *X* is finite-dimensional.^{[1]}
Each order interval in an AL-space is weakly compact.^{[1]}

The strong dual of an AL-space is an AM-space with unit.^{[1]}
The continuous dual space (which is equal to *X*^{+}) of an AL-space *X* is a Banach lattice that can be identified with , where *K* is a compact extremally disconnected topological space;
furthermore, under the evaluation map, *X* is isomorphic with the band of all real Radon measures 𝜇 on *K* such that for every majorized and directed subset *S* of we have ^{[1]}