Venter Non-tail measures

how to tell if one co-measure is marginal decomposition. As mentioned in paper, there can be many co-measures but only one marginal decomposition.

in the example of standard deviation, how would you know h(y)=y-E(Y), L(Y)=y-E(Y)/Std(Y) and r(Xj)=Cov(Xj,Y)/std(Y) is the marginal decomposition?

Thanks in advance.

Venter Non-tail measures