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Liouville's Theorem may refer to:
- Liouville's Lemma, concerning diophantine approximations.
- Liouville's Theorem (Hamiltonian Mechanics): the phase-space distribution function is constant along the trajectories of the system.
- Liouville's Theorem (Number Theory), about the transcendental nature of Liouville numbers.
- Liouville's Theorem (Differential Algebra): how to tell whether an elementary function has an elementary integral.
- Liouville's Theorem (Conformal Mappings): all conformal mappings are Möbius transformations.
- Liouville's Theorem (Complex Analysis): any bounded entire complex function is constant.