Align inside enumerate

Question

Is it possible to align \items content inside enumerateenvironment?

My expected output is:

Which I got manually, (adjusting with \hspace)

These answers:

Aligning formulas inside enumerate

Equations inside enumerate aligned on item's number

don't respond my question because they try to use align inside the \items

Neither Enumerate inside align

MWE

\documentclass{article}
\usepackage{enumitem}
\begin{document}
\begin{enumerate}
\item $X$ integrable $\Longrightarrow E[X|\mathcal{A}_1]$ integrable y $E[E[X|\mathcal{A}_1]]=E[X]$
\item $\mathcal{A}_1={\emptyset,\Omega} \Longrightarrow EX|\mathcal{A}_1=E[X],\ \forall \omega\in\Omega$
\item $\mathcal{A}_1=\mathcal{A}\Longrightarrow E[X|\mathcal{A}_1]=X \ c.s.[P_1]$ 
\end{enumerate}
\end{document}

Answer 1

I wouldn't persist with use of enumerate. Numbers can be writen for example in alignat* examle encapsulated in fleqn environment defined in the nccmath package:

\documentclass{article}
\usepackage{nccmath}
%---------------- Show page layout. Don't use in a real document!
\usepackage{showframe}
\renewcommand\ShowFrameLinethickness{0.15pt}
\renewcommand*\ShowFrameColor{\color{red}}
%---------------------------------------------------------------%
\begin{document}
\begin{fleqn}
\begin{alignat}{3}
&1.\ X \text{ integrable}\hspace{-11em} 
    &\quad&   \Longrightarrow E[X|\mathcal{A}_1] \text{ integrable y }
                    E[E[X|\mathcal{A}_1]]=E[X]                      \
&2.\ \mathcal{A}_1 ={\emptyset,\Omega} 
    &&   \Longrightarrow EX|\mathcal{A}_1=E[X],\ \forall \omega\in\Omega

                                                                    \
&3.\ \mathcal{A}_1 =\mathcal{A}
    &&   \Longrightarrow E[X|\mathcal{A}_1]=X \ c.s.[P_1]        \tag{$c.s.[P_1]$}

\end{alignat}
\end{fleqn}
\end{document}

(red lines indicate text borders)

Answer 2

Assuming this is not the only such display in your document, you might use eqparbox facilities.

\documentclass{article}
\usepackage{enumitem}
\usepackage{eqparbox}
\newcounter{mathenum}
\newenvironment{mathenum}
 {\begin{enumerate}\stepcounter{mathenum}}
 {\end{enumerate}}
\newcommand{\mathenumitem}[3]{%
  \item
  \eqmakebox[@@\themathenum @A@][l]{#1}%
  ${}\Longrightarrow{}$%
  \eqmakebox[@@\themathenum @B@][l]{#2}%
  \quad#3%
}
\begin{document}
\begin{mathenum}
\mathenumitem{$X$ integrable}
             {$E[X|\mathcal{A}_1]$ integrable y $E[E[X|\mathcal{A}_1]]=E[X]$}
             {}
\mathenumitem{$\mathcal{A}_1={\emptyset,\Omega}$}
             {$EX|\mathcal{A}_1=E[X],\ \forall \omega\in\Omega$}
             {}
\mathenumitem{$\mathcal{A}_1=\mathcal{A}$}
             {$E[X|\mathcal{A}_1]=X$}
             {c.s.$[P_1]$}
\end{mathenum}
\end{document}

A slightly different version where the central symbol (which is supposed to be an arrow) can vary:

\documentclass{article}
\usepackage{enumitem}
\usepackage{eqparbox}
\newcounter{mathenum}
\newenvironment{mathenum}
 {\begin{enumerate}\stepcounter{mathenum}}
 {\end{enumerate}}
\newcommand{\mathenumitem}[4]{%
  \item
  \eqmakebox[@@\themathenum @A@][l]{#1}%
  \eqmakebox[@@\themathenum @B@][c]{${}#2{}$}%
  \eqmakebox[@@\themathenum @C@][l]{#3}%
  \quad#4%
}
\begin{document}
\begin{mathenum}
\mathenumitem{$X$ integrable}
             {\Longrightarrow}
             {$E[X|\mathcal{A}_1]$ integrable y $E[E[X|\mathcal{A}_1]]=E[X]$}
             {}
\mathenumitem{$\mathcal{A}_1={\emptyset,\Omega}$}
             {\Longleftrightarrow}
             {$EX|\mathcal{A}_1=E[X],\ \forall \omega\in\Omega$}
             {}
\mathenumitem{$\mathcal{A}_1=\mathcal{A}$}
             {\Longleftarrow}
             {$E[X|\mathcal{A}_1]=X$}
             {c.s.$[P_1]$} 
\end{mathenum}
\end{document}