Lyapunov convexity theorem
= Lyapunov convexity theorem
{c}
The range of a finite-dimensional, finite, countably additive, atomless vector measure is <compact> and <convex>. In particular, an <atomless measure> restricted to a measurable set $E$ can realize every mass between zero and $\mu(E)$. This allows exact balancing by small disjoint consumer cohorts in an <exchange economy>.