Forget it!!!!  Trying to measure an untrue room for prefabrication of parts is nearly impossible.  Your carpenter will have to come in, establish a center line in both axis and divide the differences on the edges. This application is no different than doing a suspended ceiling, and must be done on site. There will be a bit of adjustment in all directions, I'm sure.

How to measure a crooked room?
I need to split this equation in two pages. Can you help me? Thanks

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\begin{document}
\begin{equation}
\begin{aligned}
\Theta^\diamond_o:=\{\theta &amp; \in \Theta | \\
&amp;
\begin{pmatrix}
H_l^{(1)}(x;\theta) \mathbb{P}(X=x) \leq \mathbb{P}(G_{\cdot j}=g_{\bullet}^{(1)},X=x) \leq H_u^{(1)}(x;\theta)\mathbb{P}(X=x) \\
H_l^{(2)}(x;\theta)\mathbb{P}(X=x) \leq \mathbb{P}(G_{\cdot j}=g_{\bullet}^{(2)},X=x) \leq H_u^{(2)}(x;\theta) \mathbb{P}(X=x)\\
\vdots\\
H_l^{(h)}(x;\theta)\mathbb{P}(X=x) \leq \mathbb{P}(G_{\cdot j}=g_{\bullet}^{(h)},X=x) \leq H_u^{(h)}(x;\theta)\mathbb{P}(X=x) \\
\vdots\\
H_l^{(2^{n-1})}(x;\theta)\mathbb{P}(X=x) \leq \mathbb{P}(G_{\cdot j}=g_{\bullet}^{(2^{n-1})},X=x) \leq H_u^{(2^{n-1})}(x;\theta)\mathbb{P}(X=x) \\
\end{pmatrix}\\
&amp;\forall x \in \mathcal{X}\}=\{\theta \in \Theta | \\
&amp;
\begin{pmatrix}
H_l^{(1)}(x;\theta) \mathbb{P}(X=x)-\mathbb{P}(G_{\cdot j}=g_{\bullet}^{(1)},X=x) \leq 0\\ \mathbb{P}(G_{\cdot j}=g_{\bullet}^{(1)},X=x)-H_u^{(1)}(x,n;\theta)\mathbb{P}(X=x) \leq 0\\
H_l^{(2)}(x;\theta) \mathbb{P}(X=x)-\mathbb{P}(G_{\cdot j}=g_{\bullet}^{(2)},X=x) \leq 0\\ \mathbb{P}(G_{\cdot j}=g_{\bullet}^{(2)},X=x)-H_u^{(2)}(x;\theta)\mathbb{P}(X=x) \leq 0\\
\vdots\\
H_l^{(h)}(x;\theta) \mathbb{P}(X=x)-\mathbb{P}(G_{\cdot j}=g_{\bullet}^{(h)},X=x) \leq 0\\ \mathbb{P}(G_{\cdot j}=g_{\bullet}^{(h)},X=x)-H_u^{(h)}(x;\theta)\mathbb{P}(X=x) \leq 0\\
\vdots\\
H_l^{(2^{n-1})}(x;\theta) \mathbb{P}(X=x)-\mathbb{P}(G_{\cdot j}=g_{\bullet}^{(2^{n-1})},X=x) \leq 0\\ \mathbb{P}(G_{\cdot j}=g_{\bullet}^{(2^{n-1})},X=x)-H_u^{(2^{n-1})}(x;\theta)\mathbb{P}(X=x) \leq 0\\
\end{pmatrix}\\
&amp;\forall x \in \mathcal{X}\}\subseteq\{\theta \in \Theta | \\
&amp;
\begin{pmatrix}
\sum_{x \in \mathcal{X}}^{}\left(H_l^{(1)}(x;\theta) \mathbb{P}(X=x)-\mathbb{P}(G_{\cdot j}=g_{\bullet}^{(1)},X=x)\right)\mathbb{P}(X=x) \leq 0\\ 
\sum_{x \in \mathcal{X}}^{}\left(\mathbb{P}(G_{\cdot j}=g_{\bullet}^{(1)},X=x)-H_u^{(1)}(x;\theta)\mathbb{P}(X=x)\right)\mathbb{P}(X=x)  \leq 0\\
\sum_{x \in \mathcal{X}}^{}\left(H_l^{(2)}(x;\theta) \mathbb{P}(X=x)-\mathbb{P}(G_{\cdot j}=g_{\bullet}^{(2)},X=x)\right)\mathbb{P}(X=x)  \leq 0\\ 
\sum_{x \in \mathcal{X}}^{}\left(\mathbb{P}(G_{\cdot j}=g_{\bullet}^{(2)},X=x)-H_u^{(2)}(x;\theta)\mathbb{P}(X=x)\right)\mathbb{P}(X=x)  \leq 0\\
\vdots\\
\sum_{x \in \mathcal{X}}^{}\left(H_l^{(h)}(x;\theta) \mathbb{P}(X=x)-\mathbb{P}(G_{\cdot j}=g_{\bullet}^{(h)},X=x)\right)\mathbb{P}(X=x)  \leq 0\\ 
\sum_{x \in \mathcal{X}}^{}\left(\mathbb{P}(G_{\cdot j}=g_{\bullet}^{(h)},X=x)-H_u^{(h)}(x;\theta)\mathbb{P}(X=x)\right)\mathbb{P}(X=x)  \leq 0\\
\vdots\\
\sum_{x \in \mathcal{X}}^{}\left(H_l^{(2^{n-1})}(x;\theta) \mathbb{P}(X=x)-\mathbb{P}(G_{\cdot j}=g_{\bullet}^{(2^{n-1})},X=x)\right)\mathbb{P}(X=x)  \leq 0\\ 
\sum_{x \in \mathcal{X}}^{}\left(\mathbb{P}(G_{\cdot j}=g_{\bullet}^{(2^{n-1})},X=x)-H_u^{(2^{n-1})}(x;\theta)\mathbb{P}(X=x)\right)\mathbb{P}(X=x)  \leq 0
\end{pmatrix}\\
&amp;\}=\{\theta \in \Theta | \\
&amp;
\begin{pmatrix}
\mathbb{E}_X\left(H_l^{(1)}(X;\theta) \mathbb{P}(X)-\mathbb{P}(G_{\cdot j}=g_{\bullet}^{(1)},X)\right) \leq 0\\ 
\mathbb{E}_X\left(\mathbb{P}(G_{\cdot j}=g_{\bullet}^{(1)},X)-H_u^{(1)}(X;\theta)\mathbb{P}(X)\right)\leq 0\\
\mathbb{E}_X\left(H_l^{(2)}(X;\theta) \mathbb{P}(X)-\mathbb{P}(G_{\cdot j}=g_{\bullet}^{(2)},X)\right)\leq 0\\ 
\mathbb{E}_X\left(\mathbb{P}(G_{\cdot j}=g_{\bullet}^{(2)},X)-H_u^{(2)}(X;\theta)\mathbb{P}(X)\right)\leq 0\\
\vdots\\
\mathbb{E}_X\left(H_l^{(h)}(X;\theta) \mathbb{P}(X)-\mathbb{P}(G_{\cdot j}=g_{\bullet}^{(h)},X)\right)\leq 0\\ 
\mathbb{E}_X\left(\mathbb{P}(G_{\cdot j}=g_{\bullet}^{(h)},X)-H_u^{(h)}(X;\theta)\mathbb{P}(X)\right) \leq 0\\
\vdots\\
\mathbb{E}_X\left(H_l^{(2^{n-1})}(X;\theta) \mathbb{P}(X)-\mathbb{P}(G_{\cdot j}=g_{\bullet}^{(2^{n-1})},X)\right) \leq 0\\ 
\mathbb{E}_X\left(\mathbb{P}(G_{\cdot j}=g_{\bullet}^{(2^{n-1})},X)-H_u^{(2^{n-1})}(X;\theta)\mathbb{P}(X)\right) \leq 0
\end{pmatrix}\\
&amp;\forall n \in \mathbb{N}\}
\end{aligned}
\end{equation}
\end{document}

