Trance-0/NoteNextra-origin
1
0
Fork 0
Code Issues Pull Requests Actions 1 Packages Projects Releases Wiki Activity

fix bug container may not eixsts.

Browse Source
This commit is contained in:
Zheyuan Wu
2025-04-16 10:41:04 -05:00
parent c7901188d4
commit 3d2c3afcb8
2 changed files with 16 additions and 9 deletions
Download Patch File Download Diff File Expand all files Collapse all files

4
Jenkinsfile vendored
View File

@@ -31,9 +31,9 @@ pipeline {
steps { steps {
echo "Deploying docker image ${registry}:v${version}.${env.BUILD_ID}" echo "Deploying docker image ${registry}:v${version}.${env.BUILD_ID}"
echo "Stopping existing container" echo "Stopping existing container"
sh 'docker stop notenextra' sh 'docker stop notenextra || true'
echo "Removing existing container" echo "Removing existing container"
sh 'docker rm notenextra' sh 'docker rm notenextra || true'
echo "Running new docker container" echo "Running new docker container"
sh 'docker run -d -p 13000:3000 --name notenextra ${registry}:v${version}.${env.BUILD_ID}' sh 'docker run -d -p 13000:3000 --name notenextra ${registry}:v${version}.${env.BUILD_ID}'
} }

21
pages/Math4121/Math4121_L35.md
View File

@@ -48,18 +48,25 @@ Let $F=\{x\in E: f(x)>g(x)\}$. Then $m(F)=0$.
$$ $$
\begin{aligned} \begin{aligned}
\int_E f \, dm &= \int_{E\setminus F} f \, dm + \int_F f \, dm\\ \int_E f \, dm &= \int_{E\setminus F} f \, dm + \int_F f \, dm\\
&\leq \int_{E\setminus F} g \, dm &\leq \int_{E\setminus F} g \, dm+\int_E g \, dm\\
&= \int_E g \, dm
\end{aligned} \end{aligned}
$$ $$
QED QED
#### Proposition 6.13
If $f$ is non-negative and $\int_E f \, dm =0$, then $f=0$ almost everywhere on $E$, $f(x)=0$ $\forall x\in E\setminus F$, where $m(F)=0$.
Proof:
Let $E_n=\{x\in E: f(x)\geq \frac{1}{n}\}$. Then $\frac{1}{n}\chi_{E_n}(x)\leq f(x)$ for all $x\in E$.
By definition $\frac{1}{n}m(E_n)=\int_E \frac{1}{n}\chi_{E_n} \, dm \leq \int_E f \, dm =0$.
Therefore, $m(E_n)=0$ for all $n$.
Now $U=\{x\in E: f(x)>0\}=\bigcup_{n=1}^{\infty} E_n$.
QED