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authorJustin Gassner <justin.gassner@mailbox.org>2024-02-15 05:11:07 +0100
committerJustin Gassner <justin.gassner@mailbox.org>2024-02-15 05:11:07 +0100
commit7c66b227a494748e2a546fb85317accd00aebe53 (patch)
tree9c649667d2d024b90b32d36ca327ac4b2e7caeb2 /pages/measure-and-integration/lebesgue-integral/convergence-theorems.md
parent28407333ffceca9b99fae721c30e8ae146a863da (diff)
downloadsite-7c66b227a494748e2a546fb85317accd00aebe53.tar.zst
Update
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-rw-r--r--pages/measure-and-integration/lebesgue-integral/convergence-theorems.md6
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diff --git a/pages/measure-and-integration/lebesgue-integral/convergence-theorems.md b/pages/measure-and-integration/lebesgue-integral/convergence-theorems.md
index 67f0996..f9ebc4a 100644
--- a/pages/measure-and-integration/lebesgue-integral/convergence-theorems.md
+++ b/pages/measure-and-integration/lebesgue-integral/convergence-theorems.md
@@ -32,10 +32,10 @@ $$
In the following proof we omit $X$ and $d\mu$ for visual clarity.
{% proof %}
-By definition, we have $\liminf_{n \to \infty} f_n = \lim_{n \to \infty} g_n$, where $g_n = \inf_{k \ge n} f_k$.
+By definition, we have $\liminf_{n \to \infty} f_n = \lim_{n \to \infty} g_n$,
+where $g_n = \inf_{k \ge n} f_k$.
Now $(g_n)$ is a monotonic sequence of nonnegative measurable functions.
-By the
-[Monotone Convergence Theorem](#monotone-convergence-theorem)
+By the [Monotone Convergence Theorem](#monotone-convergence-theorem)
$$
\int \liminf_{n \to \infty} f_n = \lim_{n \to \infty} \int g_n.