Named after Russian mathematician A A LYAPUNOV, Lyapunov’s theorem asserts that the range of a non-atomic totally finite vector-valued measure is both convex and compact.

Source:

A A Lyapunov, ‘On Completely Additive Vector-Functions’, Izvestia Akademii Nauk SSSR, vol. IV (1940), 465-78

**Lyapunov theorem** may refer to:

- A theorem related to Lyapunov stability – the stability of solutions of differential equations near a point of equilibrium.
- A theorem in measure theory: the range of any real-valued, non-atomic vector measure is compact and convex. See Lyapunov vector-measure theorem.
- A theorem in probability theory that establishes very general sufficient conditions for the convergence of the distributions of sums of independent random variables to the normal distribution (See Encyclopedia of mathematics).
- Several theorems in potential theory on the behaviour of potentials and the solution of the Dirichlet problem

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