some changes

inputs/lecture_10.tex

@@ -34,7 +34,7 @@ where $\mu = \bP X^{-1}$.
       \\&&
         + \lim_{T \to \infty} \frac{1}{2\pi} \int_{\R}\int_{-T}^T \frac{\sin(t ( x - b)) - \sin(t(x-a))}{-t} dt d\bP(x)\\
         &=& \lim_{T \to \infty} \frac{1}{\pi} \int_\R \int_{0}^T \frac{\sin(t(x-a)) - \sin(t(x-b))}{t} dt d\bP(x)\\
-        &\overset{\text{\autoref{fact:intsinxx}, dominated convergence}}{=}& \frac{1}{\pi} \int -\frac{\pi}{2} \One_{x < a} + \frac{\pi}{2} \One_{x > a }
+        &\overset{\substack{\text{\autoref{fact:intsinxx},}\\\text{dominated convergence}}}{=}& \frac{1}{\pi} \int -\frac{\pi}{2} \One_{x < a} + \frac{\pi}{2} \One_{x > a }
                                                                 - (- \frac{\pi}{2} \One_{x < b} + \frac{\pi}{2} \One_{x > b}) d\bP(x)\\
         &=&  \frac{1}{2} \bP(\{a\} ) + \frac{1}{2} \bP(\{b\}) + \bP((a,b))\\
         &=& \frac{F(b) + F(b-)}{2} - \frac{F(a) - F(a-)}{2}

inputs/lecture_11.tex

@@ -116,7 +116,7 @@ If $S_n \sim \Bin(n,p)$ and $[a,b] \subseteq  \R$, we have
     $\bP[|S_n - np| \le  0.01 n] \le  0.05$.
     We have that
     \begin{IEEEeqnarray*}{rCl}
-        &&\bP[|S_n - nü| \le  0.01n] \\
+        &&\bP[|S_n - np| \le  0.01n] \\
         &=& \bP[ -0.01 n \le  S_n - np \le  0.01n]\\
         &=& \bP[-\frac{0.01 n}{\sqrt{n p (1-p)} } \le  \frac{S_n - np}{\sqrt{n p (1-p)} } \le \frac{0.01 n}{\sqrt{n p (1-p)}}\\
         &\approx& \Phi(0.01 \sqrt{\frac{n}{p(1-p)}}) - \Phi(-0.01 \sqrt{\frac{n}{p(1-p)}})\\

wtheo.sty

@@ -93,3 +93,6 @@
 
 \NewFancyTheorem[thmtools = { style = thmredmargin} , group = { big } ]{warning}
 \DeclareSimpleMathOperator{Var}
+\DeclareSimpleMathOperator{Exp}
+\DeclareSimpleMathOperator{Bin}
+\DeclareSimpleMathOperator{Ber}