  Given a square integrable m-dimensional random variable $X$ on a probability
space $(\Omega.\mathcal F,\Pr)$ and a sub sigma algebra $\mathcal A$, we show
that there exists another m-dimensional random variable $Y$, independent of
$\mathcal A$ and minimising the $L^2$ distance to $X$. Such results have an
importance to fairness and bias reduction in Artificial Intelligence, Machine
Learning and Network Theory.
