deletions | additions       diff --git a/We_are_now_ready_to__.tex b/We_are_now_ready_to__.tex  index ca9c85a..9c06f84 100644  --- a/We_are_now_ready_to__.tex  +++ b/We_are_now_ready_to__.tex 
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\begin{equation}  \E_{(x,y) \sim \mu^k \E_{\mu^k  \times U^{\R_P(K)}}[(P^{kj}(x,y) U^{\R_P(K)}}[(P^{kj}  - f(x))^2] f)^2]  \leq \E_{(x,y) \sim \mu^k \E_{\mu^k  \times U^{\R_Q(K)}}[(Q^{kj}(x,y) U^{\R_Q(K)}}[(Q^{kj}  - f(x))^2] f)^2]  + \varepsilon(k,j) \end{equation}