Ack, I think you’re right. I think I need to replace the assumption that 𝔼₁[Z | Y≥c] = 𝔼₂[Z | Y≥c] with the assumption that ℙ₁[(Y,Z)|Y≥c] = ℙ₂[(Y,Z)|Y≥c] which will guarantee the equality you’re pointing out is true for all f. This seems totally fine since it’s just a construction, but it definitely looks like an error to me. I’ll fix that, thank you!
Ack, I think you’re right. I think I need to replace the assumption that 𝔼₁[Z | Y≥c] = 𝔼₂[Z | Y≥c] with the assumption that ℙ₁[(Y,Z)|Y≥c] = ℙ₂[(Y,Z)|Y≥c] which will guarantee the equality you’re pointing out is true for all f. This seems totally fine since it’s just a construction, but it definitely looks like an error to me. I’ll fix that, thank you!