deletions | additions       diff --git a/The_following_theorem_is_the__.tex b/The_following_theorem_is_the__.tex  index 25d72de..3d24b67 100644  --- a/The_following_theorem_is_the__.tex  +++ b/The_following_theorem_is_the__.tex 
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$$\E_{\mu^k \times U^{\R_P(k,j)}}[(P^{kj} - f)^2] \leq \E_{\mu^k \times U^{\R_S(k,j)}}[(P^{kj} + t(k,j)S^{kj} + \varepsilon_t^{kj} - f)^2] + \varepsilon(k,j)$$  $$\E_{\mu^k \times U^{\R_P(k,j)}}[(P^{kj} $$\E[(P^{kj}  - f)^2] \leq \E_{\mu^k \times U^{\R_S(k,j)}}[(P^{kj} \E[(P^{kj}  + t(k,j)S^{kj} - f)^2] + 2 \E_{\mu^k \times U^{\R_S(k,j)}}[(P^{kj} \E[(P^{kj}  + t(k,j)S^{kj} - f) \varepsilon_t^{kj}] + \E_{\mu^k \times U^{\R_S(k,j)}}[(\varepsilon_t^{kj})^2] \E[(\varepsilon_t^{kj})^2]  + \varepsilon(k,j)$$ BLAH