 ##  [Liouville's Theorem](/liouvilles-theorem) 

  ##  [Liouville's Theorem](https://mathlogic.quantumdictionary.io/liouvilles-theorem-0) 

  
 [![Mathematics & Logic Dictionary](/sites/default/files/styles/large/public/2026-01/Mathematics%20%26%20Logic.png.webp?itok=UhtTRPnp)](/topic-specific-dictionaries/natural-formal-sciences/mathematics-logic)

- Natural &amp; Formal Sciences -

**Mathematics &amp; Logic Dictionary**

 
Definition

A result in complex analysis stating that any entire (holomorphic on the whole complex plane) function that is bounded must be constant.