deletions | additions       diff --git a/The_following_theorem_is_the__.tex b/The_following_theorem_is_the__.tex  index 8696535..9ee1ccf 100644  --- a/The_following_theorem_is_the__.tex  +++ b/The_following_theorem_is_the__.tex 
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\begin{theorem}  \label{thm:ort}  Fix $\Gamma$ a growth space of type $(2,2)$ and $\mathcal{E}$ and error space of rank 2. Assume there is $\zeta \in \mathcal{E}$ s.t. $\log $(0,\log  \max(-\log \zeta, 1) 1))  \in \Gamma$\footnote{If $(0, \log(k+1)), (0, \log(j+1)) \in \Gamma$ then this condition holds for any $\mathcal{E}$ since we can take $\zeta = 2^{-h}$ for $h$ polynomial.}. Consider $(\mu,f)$ a distributional estimation problem and $P$ an $\mathcal{E}(\Gamma)$-optimal predictor for $(\mu,f)$. Then, $P$ is also an $\mathcal{E}^{\frac{1}{2}\sharp}(\Gamma)$-optimal predictor for $(\mu,f)$. \end{theorem}