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Revision as of 17:37, 31 January 2019 by Deansg(talk | contribs)(Distinguish from Lindelöf's lemma in topology)
Suppose that ƒ is holomorphic (i.e. analytic) on Ω and that there are constants M, A and B such that
and
Then f is bounded by M on all of Ω:
Proof
Fix a point inside . Choose , an integer and large enough such that
. Applying maximum modulus principle to the function and
the rectangular area we obtain , that is, . Letting yields
as required.