Morera's Theorem
In two variable Calculus, you learnt the following result: let
and
be two functions defined on the same simply connected domain
. Suppose that
and
are continuous on the interior of
and that, for every Jordan curve in
, the following equation holds:
Then
in
.
Using this result we can prove the following converse to Cauchy-Goursat
theorem:
Proposition 5.6.1
Let
be a function such that
are continuous in a simply connected domain
. Suppose that, for every Jordan curve in
, the integral
is equal to 0. Then
is analytic on
.
Another converse of Cauchy-Goursat theorem, stronger than Proposition 6.1
is Morera's theorem:
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