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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 vector measure#Lyapunov's 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 (See Encyclopedia of mathematics).
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