deletions | additions       diff --git a/We_are_now_ready_to__.tex b/We_are_now_ready_to__.tex  index 9575227..06ce279 100644  --- a/We_are_now_ready_to__.tex  +++ b/We_are_now_ready_to__.tex 
...
Fix $\Gamma$ a growth space of type $(2,2)$ and $\mathcal{E}$ and error space of rank 2. Consider $(\mu,f)$ a distributional estimation problem and $P: \Words \xrightarrow{\Gamma} \Rats$ with bounded range. $P$ is called an \emph{$\mathcal{E}(\Gamma)$-optimal predictor for $(\mu,f)$} when for any $Q: \Words \xrightarrow{\Gamma} \Rats$ there is $\varepsilon \in \mathcal{E}$ s.t.  \begin{equation}  a^2 + b^2 = c^2  \end{equation}  \begin{equation} \E_{\mu^k \times U^{\R_P(k,j)}}[(P^{kj} - f)^2] \leq \E_{\mu^k \times U^{\R_Q(k,j)}}[(Q^{kj} - f)^2] + \varepsilon(k,j) \end{equation}  \end{definition}