convergence_implications.tex

\documentclass[tikz, margin=3.14mm]{standalone}
\usetikzlibrary{cd, backgrounds}

% advice to use pagecolor{white} from:
% https://tex.stackexchange.com/questions/529903/tikzcd-crossing-over-background-color 
\pagecolor{white}

% advice on using column sep = normal for tikz-cd in a standalone from:
% https://tex.stackexchange.com/questions/499162/tikzcd-incompatible-with-standalone-document-class 

\begin{document}
\begin{tikzcd}[column sep=normal,
    background color=white]
    X_n \stackrel{a.s.}{\longrightarrow} X \arrow[Rightarrow, dr] & & \\
    & X_n \stackrel{p}{\longrightarrow} X \arrow[Rightarrow, r] &  X_n \stackrel{d}{\longrightarrow} X \\ 
    X_n \stackrel{\mathcal L_p}{\longrightarrow} X \arrow[Rightarrow, ur] & 
\end{tikzcd}
\end{document}