diff --git a/inputs/a_2_additional_stuff.tex b/inputs/a_2_additional_stuff.tex index 8d7f910..26bf3fa 100644 --- a/inputs/a_2_additional_stuff.tex +++ b/inputs/a_2_additional_stuff.tex @@ -15,18 +15,17 @@ boundedness we used in the lecture. \item \vocab{dominated by $f \in L^p$} for $p \ge 1$ iff \[ \forall X \in \cX .~ |X| \le f, - \] + \] \item \vocab{bounded in $L^p$} for $p \ge 1$ iff \[ \sup_{X \in \cX} \|X\|_{L^p} < \infty, - \] + \] \item \vocab{uniformly integrable} iff \[ \forall \epsilon > 0 .~\exists K .~ \forall X \in \cX.~ \bE[|X| \One_{|X| > K}] < \epsilon. - \] + \] \end{itemize} - \end{definition} \begin{fact}+