deletions | additions       diff --git a/The_following_theorem_is_the__.tex b/The_following_theorem_is_the__.tex  index 40351f1..0750523 100644  --- a/The_following_theorem_is_the__.tex  +++ b/The_following_theorem_is_the__.tex 
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$$\E_{\mu^k \times U^{\R_P(k,j)}}[(P^{kj} - f)^2] \leq \E_{\mu^k \times U^{\R_S(k,j)}}[(Q_t^{kj} - f)^2] + \varepsilon(k,j)$$  Using (\ref{eqn:thm-ort-prf1}) (\ref{eqn:thm:ort:prf1})  $$\E_{\mu^k \times U^{\R_P(k,j)}}[(P^{kj} - f)^2] \leq \E_{\mu^k \times U^{\R_S(k,j)}}[(P^{kj} + t(k,j)S^{kj} - f)^2] + \varepsilon(k,j) + 2^{-h(k,j)}$$