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Mathematics
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Complex Analysis
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Morera's Theorem
Morera's Theorem
📜
The statement of the theorem
If
f
f
f
is continuous in a domain
D
D
D
and
∮
γ
f
(
z
)
d
z
=
0
\oint_\gamma f(z) dz = 0
∮
γ
f
(
z
)
d
z
=
0
for every closed curve
γ
\gamma
γ
in
D
D
D
, then
f
f
f
is holomorphic in
D
D
D
.
Source: Wikipedia