Editing Morera's theorem (section)

==Weakening of hypotheses==
The hypotheses of Morera's theorem can be weakened considerably.  In particular, it suffices for the integral
<math display="block">\oint_{\partial T} f(z)\, dz</math>
to be zero for every closed (solid) triangle ''T'' contained in the region ''D''. This in fact [[characterization (mathematics)|characterizes]] holomorphy, i.e. ''f'' is holomorphic on ''D'' if and only if the above conditions hold. It also implies the following generalisation of the aforementioned fact about uniform limits of holomorphic functions: if ''f''<sub>1</sub>,&nbsp;''f''<sub>2</sub>,&nbsp;... is a sequence of holomorphic functions defined on an open set {{math|Ω ⊆ '''C'''}} that converges to a function ''f'' uniformly on compact subsets of Ω, then ''f'' is holomorphic.