Yup, that’s exactly the right idea, and indeed constructing Ω by just taking a tuple of all the redund Γ‘s (or a sufficient statistic for that tuple) is a natural starting point which works straightforwardly in the exact case. In the approximate case, the construction needs to be modified—for instance, regarding the third condition, that tuple of Γ’s (or a sufficient statistic for it) will have much more entropy conditional on X than any individual Γ.
Yup, that’s exactly the right idea, and indeed constructing Ω by just taking a tuple of all the redund Γ‘s (or a sufficient statistic for that tuple) is a natural starting point which works straightforwardly in the exact case. In the approximate case, the construction needs to be modified—for instance, regarding the third condition, that tuple of Γ’s (or a sufficient statistic for it) will have much more entropy conditional on X than any individual Γ.