Consider adding more context at the beginning of the post about why the reader should care. Something like:
“Finite factored sets have the fundamental theorem, which is X. This is an analogous theorem but for the more general case of using measurable spaces. It is formulated using the causal graph construction.”
This is important because it allows us to solve “Concrete problem P” which we were not able to solve before. (Or whatever the reason is that this is progress.) An alternative to this would be to first introduce a problem that is clearly important and then show how finite factored sets can’t handle this problem very well.
Of course, if there are writeups doing these things you may supplement links to them. Though even then it is probably good to give a very brief summary still.
I think making these changes would be almost no work, compared to doing all the math, and it would make it a lot more accessible. Right now this text seems to assume that you are intimately familiar with finite factored sets, to the extent that you would not even look up again what the fundamental theorem for finite factored sets is (there is no link to it at the appropriate point).
As I don’t quite understand what you did, some of the details in my suggestions might be wrong, but I think the overall points I am trying to make should still hold up.
Consider adding more context at the beginning of the post about why the reader should care. Something like:
“Finite factored sets have the fundamental theorem, which is X. This is an analogous theorem but for the more general case of using measurable spaces. It is formulated using the causal graph construction.”
This is important because it allows us to solve “Concrete problem P” which we were not able to solve before. (Or whatever the reason is that this is progress.) An alternative to this would be to first introduce a problem that is clearly important and then show how finite factored sets can’t handle this problem very well.
Of course, if there are writeups doing these things you may supplement links to them. Though even then it is probably good to give a very brief summary still.
I think making these changes would be almost no work, compared to doing all the math, and it would make it a lot more accessible. Right now this text seems to assume that you are intimately familiar with finite factored sets, to the extent that you would not even look up again what the fundamental theorem for finite factored sets is (there is no link to it at the appropriate point).
As I don’t quite understand what you did, some of the details in my suggestions might be wrong, but I think the overall points I am trying to make should still hold up.