Definition: We say that C’s agent can observe a finite partition V of W if for all functions f:V→A, there exists an element af∈A such that for all e∈E, f(v(af⋅e))⋅e=af⋅e.
Claim: This definition is equivalent to the definition from subsets.
This doesn’t hold in the degenerate case W=∅, since then we have an empty function f but no elements of A. (But the definition from subsets holds trivially.)
This doesn’t hold in the degenerate case W=∅, since then we have an empty function f but no elements of A. (But the definition from subsets holds trivially.)
This was annoying to fix, so I just made W nonempty in the intro to the post.