Liouville's theorem
(Redirected from Bounded and entire implies constant)
This article gives the statement, and possibly proof, of a basic fact in complex analysis.
View a complete list of basic facts in complex analysis
Name
This result is termed Liouville's theorem in complex analysis. However, the term Liouville's theorem is also used for theorems proved by Liouville in other parts of mathematics.
Statement
Any entire function (holomorphic function on the whole of ) that is bounded (i.e. its image is bounded in absolute value) must be constant.
