Multivariate Context:

Taking into account the long and short positions, in the multivariate case we introduce notation $\mu^{\pm_{(P)}}$ to denote a generic measure, $\mu$, associated with a specific portfolio and position. Using this notation, we can then construct the mean measure, $\mu_m$,in the multivariate (m) context as  

$$\mu_m = {1\over2}\left(\mu^{+_{(P)}} + \mu^{-_{(P)}}\right)$$ (2)

where each $\mu^{\pm_{(P)}}$ is an intrinsically multivariate construct related to the 2 distinct portfolios with respect to which loss is estimated by a candidate model.