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There is a variant of definition ~\ref{def:op} which is nearly equivalent and is often useful.   We can think of functions $f: \Supp \mu \rightarrow \Reals$ as vectors in a real Hilbert inner product  space with inner product $\Chev{f,g}:=\E_\mu[fg]$. Informally, we can think of $\Gamma$-schemes as a subspace (although a $\Gamma$-scheme is not even a function) and an $\mathcal{E}(\Gamma)$-optimal predictor for $(\mu,f)$ as the nearest point to $f$ in this subspace. Now, given a Hilbert space $H$, an inner product $V$,  a vector $f \in H$, V$,  an actual subspace $V $W  \subseteq H$ V$  and $p = \Argmin{q \in V} W}  \Norm{q - f}^2$, we have $\forall v \in V: W:  \Chev{v,p-f}=0$.