The paper under review investigates the Fatou property, i.e., lower semicontinuity for bounded convergence, of risk measures on a general law-invariant (or rearrangement-invariant) domain $\Cal X$. The main result is Theorem 2.2, where it is shown that the Fatou property can be automatically guaranteed for convex or coherent risk measures on $\Cal X$ based on a property of the underlying domain $\Cal X$, and this property is called the almost order continuous equidistributional average (AOCEA) property. The Fatou property guarantees dual representation of convex risk measures.