deletions | additions       diff --git a/The_following_theorem_is_the__.tex b/The_following_theorem_is_the__.tex  index 0750523..8134a08 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 Denoting $\varepsilon^{kj}_t(x,y,z):=Q_t^{kj}(x,yz) - P^{kj}(x,y) - t(k,j) S^{kj}(x,yz)$ and using  (\ref{eqn:thm:ort:prf1}) $$\E_{\mu^k \times U^{\R_P(k,j)}}[(P^{kj} - f)^2] \leq \E_{\mu^k \times U^{\R_S(k,j)}}[(P^{kj} + t(k,j)S^{kj} + \varepsilon^{kj}_t(x,y,z)  - f)^2] + \varepsilon(k,j) + 2^{-h(k,j)}$$ BLAH