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authorJustin Gassner <justin.gassner@mailbox.org>2024-02-29 17:32:24 +0100
committerJustin Gassner <justin.gassner@mailbox.org>2024-02-29 17:32:24 +0100
commita1b5de688d879069b5e1192057d71572c7bc5368 (patch)
treea0f4801d14bfbcc75a6091bdc7d17aceab71f6d4 /pages/complex-analysis/one-complex-variable/cauchys-theorem.md
parent8b9bb9346c217874670b0f1798ab6f1cb28fdb83 (diff)
downloadsite-a1b5de688d879069b5e1192057d71572c7bc5368.tar.zst
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+++ b/pages/complex-analysis/one-complex-variable/cauchys-theorem.md
@@ -7,7 +7,7 @@ nav_order: 2
# {{ page.title }}
-{% theorem Cauchy's Theorem (Homotopy Version) %}
+{% theorem Cauchy’s Theorem (Homotopy Version) %}
Let $G$ be a connected open subset of the complex plane.
Let $f : G \to \CC$ be a holomorphic function.
If $\gamma_0$, $\gamma_1$ are homotopic closed curves in $G$, then
@@ -29,7 +29,7 @@ $$
{{ page.title }} has a converse:
-{% theorem * Morera's Theorem %}
+{% theorem * Morera’s Theorem %}
Let $G \subset \CC$ be open and let $f : G \to \CC$ be a continuous function.
If $\int_{\gamma} f(z) \, dz = 0$ for every contour $\gamma$ contained in $G$,
then $f$ is holomorphic in $G$.