lecture 10 thm 5

inputs/lecture_10.tex

@@ -154,7 +154,8 @@ However, Fourier analysis is not only useful for continuous probability density
     Let $\phi$ be the characteristic function of $\bP \in M_1(\lambda)$.
     Then
     \begin{enumerate}[(a)]
-        \item $\phi(0) = 1$, $|\phi(t)| \le 1$ and $\phi(\cdot )$ is continuous.
+        \item $\phi(0) = 1$, $|\phi(t)| \le 1$, $\phi(-t) = \overline{\phi(t)}$
+            and $\phi(\cdot )$ is continuous.
         \item $\phi$ is a \vocab{positive definite function},
             i.e.~
             \[\forall t_1,\ldots, t_n \in \R, (c_1,\ldots,c_n) \in \C^n ~ \sum_{j,k = 1}^n c_j \overline{c_k} \phi(t_j - t_k) \ge  0