Mean-zero L2 space
= Mean-zero L2 space
{title2=$L^2_0(P)=\{h\in L^2(P):Ph=0\}$}
The mean-zero L2 space is the kernel of the <bounded linear functional> $h\mapsto Ph$ on <L2 space> for a <probability measure> $P$. It is a <closed subspace of a Hilbert space>, with <inner product> $P(hk)$, and is the natural ambient space for <score functions> and <canonical gradients>.