Thank you for your comment! You are right, these things are not clear from this post at all and I did not do a good job at clarifying that. I’m a bit low on time atm, but hopefully, I’ll be able to make some edits to the post to set the expectations for the reader more carefully.
The short answer to your question is: Yep, X is the space of events. In Vanessa’s post it has to be compact and metric, I’m simplifying this to an interval in R. And P+/P− can be derived from PHg by plugging in g=0 and replacing the measure m(A) by the Lesbegue integral ∫Adm. I have scattered notes where I derive the equations in this post. But it was clear to me that if I want to do this rigorously in the post, then I’d have to introduce an annoying amount of measure theory and the post would turn into a slog. So I decided to do things hand-wavy, but went a bit too hard in that direction.
Thank you for your comment! You are right, these things are not clear from this post at all and I did not do a good job at clarifying that. I’m a bit low on time atm, but hopefully, I’ll be able to make some edits to the post to set the expectations for the reader more carefully.
The short answer to your question is: Yep, X is the space of events. In Vanessa’s post it has to be compact and metric, I’m simplifying this to an interval in R. And P+/P− can be derived from PHg by plugging in g=0 and replacing the measure m(A) by the Lesbegue integral ∫Adm. I have scattered notes where I derive the equations in this post. But it was clear to me that if I want to do this rigorously in the post, then I’d have to introduce an annoying amount of measure theory and the post would turn into a slog. So I decided to do things hand-wavy, but went a bit too hard in that direction.