Liouville's theorem

American  

noun

Mathematics.

1. the theorem that every function of a complex variable, bounded and differentiable for all finite values of the variable, is a constant function.

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Etymology

Origin of Liouville's theorem

Named after J. Liouville

Example Sentences

In a physical system if we represent by q one of the generalized coordinates and by p the corresponding momentum, according to Liouville’s theorem the domain ∫∫dpdq, considered at given instant, is invariable with respect to the time if p and q vary according to Hamilton’s equations.

From Project Gutenberg